Most of the answers in this thread and around the web say, "Then stop looking at the screen for so long." But I am here to say there is absolutely something else going on here. It seems that everyone is reacting slightly differently, so I don't know if we'll be able to find one grand unifying cause for this, but here's my experience:
 
I bought an rMBP about 6 weeks ago and moved from my Toshiba Satellite running Windows 7. Within a few days I had terrible eyestrain. The eyestrain persists whether I look at the Retina display itself or plug it into an external monitor (I've tried several). I've tried every intervention known to man (including seeing a retina specialist) but the only thing that helps is not using it. I can go back to the Windows laptop and the strain DISAPPEARS with no change in viewing conditions or duration. I can also read on my Retina iPad for hours and have no strain. It is inexplicable.
 
So here are all the theories I could find floating around the web about what it could be. I've tested most of them and have come up empty-handed, but your mileage may vary. I hope at some point in the future someone at Apple has an Aha! moment and figures out what their screens are doing to people.
 
Convergence/Accommodative Stress
This is part of the tired old "stop staring at the screen" argument. To focus on a near object, our eyes must both accommodate (ciliary muscles) and converge (angle inward). Over time, this can generate strain and tension in the eye muscles. One quackish doctor even invented a piece of headgear called a myopter to eliminate both of these stresses in children with reading trouble. However, while a valid concern for computer users in general, this cannot possibly cause a problem with one computer and not with another positioned in the same exact location on the desk. Plus, I did eye exercises, got reading glasses, and moved the computer back and forth to no avail. Next.
 
Dry Eye/Blinking
Again, this falls in the camp of "then why didn't I have a problem before?" Staring at a screen causes one to blink less frequently, resulting in dry eyes. I have been using eye drops but they haven't helped.
 
Glare
rMBPs have a glossy screen that shows a perfect specular reflection. Some people are sensitive to this, as their eyes become confused and try to focus on the glare instead of the image. Some common interventions are tilting or moving the screen or getting a screen protector. This was not the problem in my case, as my old laptop also has a glossy screen and I can tolerate a high degree of glare.
 
Brightness Too High
rMBP screens are bright and sharp, and sometimes very bright lights can cause eyestrain (think of snow on a sunny day). Lowering the brightness (with automatic brightness adjustment turned off) didn't help in my case. I also tried OSX' "Dark Mode," which inverts the menu bar and a few other interface components. No luck.
 
Brightness Too Low
Sometimes too dim a screen can cause strain and squinting, or artifacts from pulse-width modulation (see below). Raising the brightness didn't help in my case.
 
Dot Pitch
Retina displays have much smaller pixels than traditional displays... that's the point. They are supposed to be small enough to be imperceptible to the eye. One theory is that some people's eyes/brains are trained to lock onto a visible pixel grid, and when this is taken away, their reflex of accommodation (focusing) continually searches and strains to find that reference point. I tried creating a wallpaper image that made the pixel grid apparent, both for the Retina display and for the external monitor. It didn't help.
 
Font Size
Reading smaller print can cause eyestrain. However, increasing the size of the fonts in Google Chrome did not reduce eyestrain for me.
 
Pulse-Width Modulation (PWM)
Since LEDs can't be dimmed by reducing their voltage, some LED screens use a technology called PWM to flicker the backlight of the screen on and off extremely rapidly to create the illusion of dimming. One possible solution is to turn the screen's brightness up to 100% to eliminate the flickering. However, it doesn't appear that current rMBPs use this technology (or their flicker is so fast, in the thousands of Hz, to render it absolutely imperceptible). I placed the computer behind an electric fan to serve as a makeshift stroboscope and could not see any flicker artifacts.
 
LCD 60Hz AC Flicker
LCD screens can flicker at 60Hz because this is the frequency of the alternating current (AC) coming from the wall. This isn't an issue with the rMBP because it uses an LED screen, which doesn't suffer from AC flicker.
 
Refresh Rate
This is a controversial one. Old CRT monitors used to scan the entire screen at a certain rate (60–85Hz) to light up all the pixels. After their initial fluorescence, the phosphors would dim slightly before the next refresh, causing the screen to flicker. 60Hz flicker caused eyestrain for some people (including me), while faster rates such as 85Hz relieved it. With LED screens, there is no sequential scanning, nor phosphors to fluoresce and dim. Therefore many vehemently dismiss this as a cause. BUT! Read on!
 
OSX Frame Rate
Somewhere in the bowels of OSX and the onboard video cards I think the Mac is hard-coded to deliver animation frames to the display 60 times per second (60Hz) when scrolling windows, minimizing, etc. So even though the screen is not flickering at 60Hz, all events happening on the display are quantized to 60Hz. Could this be the culprit? I don't know. As far as I know this cannot be changed, so I couldn't test it.
 
Temporal Dithering
Apple presumably uses a technology called temporal dithering to display certain colors that are out of the gamut of its panels. This technology flips the color of a pixel back and forth between two colors very quickly to produce the appearance of a third, out-of-gamut color. Using this allows a 6-bit display (with a faster response time) to show 8 bits' worth of color (or more). However, it's almost impossible to find out much information on which models of MBPs use this technology, or anything else about it. I suspect that, if it's happening, the dithering is taking place at 60Hz, which could explain the "snow" effect some people see when looking at a white rMBP screen. But I have no proof. There is also no way to turn it off, although the folks at Amulet Hotkey wrote a kernel hack to do so (which they wouldn't pass on to me), so I know it's at least possible for someone with a high degree of technical knowledge. I don't know if this is happening at the video card level or the OSX level. I did hear that it might be possible to "wash" the dithering out of the signal by using a digital-analog conversion. I bought an HDMI to VGA converter and plugged in my external monitor, but it made no difference in eye comfort. I also tried a utility that allowed me to control which of my two video cards was being used in the hopes that maybe one of them had a driver that was causing the problem. No luck. The last thing I tried here was using the "Increase Contrast" setting in System Preferences to crank the contrast up all the way and hopefully prevent the Mac from trying to display any out-of-gamut colors. I can't say if it helped or not, but it sure did make the computer unusable.
 
Spectrum Spikes
Regular white light consists of a flat spectrum, or roughly equal amounts of each visible color. Computer screens, on the other hand, deliver a high-powered "spike" at red, green, and blue, and little energy at other frequencies. Since our eyes mainly see red, green, and blue, the visual effect is similar, but some have hypothesized that this unnatural energy distribution can cause eyestrain, damage, and a host of other effects. Why this would set the rMBP apart from any other RGB display, though, is unclear, unless perhaps their screens have slightly DIFFERENT RGB color coordinates than other screens. I doubt they could be very different, though, without messing up the color reproduction. I don't have direct data for this.
 
Blue Light/UV Light
Another closely related theory is that the screens deliver too much light in the blue or UV portion of the spectrum. Blue light has a shorter wavelength and thus higher energy than red or green, and can cause more radiative damage because of this. It can also cause disruptions in the circadian rhythm, making it more difficult to sleep. There are a few interventions to counteract this. F.lux is an app that changes the color temperature of the display towards the yellow/orange end and can vary it based on the time of day. The Gunnar company sells yellow-tinted glasses that reduce the amount of blue light. Crizal also offers a line of lenses called Prevencia that filter out UV and reduce glare without tinting the color. I used the f.lux app on my old computer and tried it on the new one, but it made no difference.
 
Quartz vs. ClearType
Windows uses the ClearType algorithm to antialias its type. ClearType cheats the shape and spacing of the letterforms so that vertical and horizontal strokes land directly on the center of a row or column of pixels, making them 100% activated. It gives a more pixellated look. Mac OSX, on the other hand, uses the Quartz type rendering engine. Quartz stays true to the shape and spacing of the letterforms while sacrificing some sharpness. While more attractive and more faithful, this makes the pixellation of Mac type less predictable to the eye, as a vertical stroke might be one, two, or more pixels wide at varying levels of intensity. Some people perceive this as blurry. OSX used to (<=10.9) allow for turning this off at lower type sizes but as of Yosemite this has been removed. The amount of smoothing can be adjusted to one of four levels (0–3) using a Terminal command (http://osxdaily.com/2010/02/18/c...) but not completely eliminated. Playing with this setting did not help me, although it's interesting that the iPad is pixel-identical to the rMBP and yet causes no eyestrain. And also that a screen capture of Mac text, viewed on Windows, does appear blurry. This might be at least part of the problem for me, but certainly not all of it.
 
Helvetica
Starting in 10.10 Yosemite, OSX changed its system font from Lucida Grande to Helvetica to match iOS more closely. There was debate as to its readability compared with Lucida Grande. I installed an app that somehow managed to revert the system font to Lucida Grande (I never used a Mac before 10.10). It didn't help.
 
Bluetooth/EMF
I read a few reports that certain people can actually perceive a Bluetooth signal and that it can make them feel sick. Turning off Bluetooth didn't make a difference for me.
 
Trigger Points
Trigger points are small, hard knots within muscle fibers that become stuck in a contracted state due to overuse. They are often painless but can cause referred pain or other symptoms at other locations in the body. Trigger points sometime belie their presence by twitching when pressure is applied. Trigger points in the sternocleidomastoid muscles (SCM) in the front of the neck have been implicated in headache, neck tightness, and visual disturbances, as have several other muscles in the head. Poor posture, stress, lack of sleep, bruxism, injury, and inactivity can all cause or worsen trigger points. And while doing some self-massage on these muscles, I did find and deactivate several of them. But it did not make a difference to my Mac-induced eyestrain.
 
Brain Tumors and Other Actual Health Problems
I hate to mention it, but brain tumors can actually cause blurred vision and other vision problems. So can macular degeneration, retinal detachment, cataracts, presbyopia, accommodative spasm, thyroid disorders, and a host of other diseases. As for me, I have been checked up by two eye doctors and an ER doctor and am fine. My thyroid medication is under control. Plus, what are the odds that I have some magical health problem that appeared when I bought the Mac and goes away every time I spend more than a couple hours away from it?
 
Spiritual Problems
People, places, and things can be under the influence of demons due to sin. Since I bought this computer used, I wondered if this might be a problem from the previous owner. However, I had the rMBP blessed by a Catholic priest and also offered it to Jesus in the Blessed Sacrament, and it was no easier to look at afterward.
 
Psychological Trouble
Sometimes this all does make me feel as if I'm going insane. And I have no proof that my trouble with this Mac is not psychosomatic. Negative thoughts and stress can produce or worsen physical symptoms. However, I doubt it, because I was really, really looking forward to switching to Mac, and I am strongly biased towards it. I love the way the screen looks. The type is amazing. The responsiveness of the computer, the convenience of QuickLook... I could go on and on about all the attributes that made me want to try it. But at the end of the day, there are two computers sitting side-by-side on my desk. One of them is boring holes in my face. I think, unfortunately, the MacBook will be sold.
 
I hope this post may give others a place to start when diagnosing this problem. I also hope that there will eventually be a solution.