Oooh, I love this stuff.
Technical crap for those that want to understand this topic at a granular level:
(Taken from the 2nd image, the nicer of the two)
Bickering aside, as one can see, the the scaled pixels alternate between 5x5, 5x6, 6x6 and 6x5 when that image is scaled up to 1320x880. It looks okay to the untrained eye, and it's kind of annoying to the folks who notice it, but what they're noticing is pixel scaling. With that said, there's not a whole lot you can control about it. Period. That's kind of how you have to look at it, because it depends completely the display resolution of the physical monitor itself and what it's capabilities are. It's an unknown variable.
With portable consoles, pixel scaling is always 1:1 because the screens are still relatively small enough that they don't require scaling. What you absolutely can control is the aspect ratio, which is what Jude was talking about. If you are developing from the ground up, you can take aspect ratio into account to figure out your desired scaling preference. JS is right in that by picking the right resolution that works for your game, you can minimize undesirable pixel scaling while still maximizing common screen ratios.
For instance, GBA games are 240x160, which is a 3:2 ratio, nonstandard for PCs... so scaling that up to 1920 width (800%) would require a height of 1280 (higher than 16:10's 1200px, and 16:9's 1080px). Let's say you had a 16:10 monitor. In order to see the whole picture in the correct aspect ratio, you have to scale it to the height of 1200, making the width 1800 (750%). 1800x1200 isn't a standard windows resolution, so, it has to use 1920x1200, but pads it with black bars on the left & right (pillarboxing) to retain that aspect ratio. If you absolutely had to have 1:1 pixel scaling, the closest you could get in that case would be 1680x1120 (700%), where you'd end up with both pillarboxing and letterboxing (top/bottom) in a 1920x1200 display resolution.
SNES emulation has the same problem. The console itself was 256x224, which does not scale up cleanly to a resolution such as 1920x1200 or 1920x1080, so you end up with black bars all around the image. If you were to scale it to the height of that 16:10 screen, you'd only have pillarboxing, but the pixels would be scaled by something like 535% and get that alternating pattern effect of distorted pixels. This looked gnarly back in the day when people had screens that were 800x600, but it's not so bad these days with much higher resolutions.
RM Specific:
This ties a little into what JS was saying about choosing "640 x 352 which is the closest to 640x360 (16:9) that still supports whole tiles." This is actually a great topic in and of itself, because choosing the resolution in tile-based games impacts whether you can display the character in the direct center of the screen (VX Ace) vs. off to the side (2k/3/XP) In 2k3, the screen of course was 320x240, and always showed 20x15 tiles when the character wasn't moving (offset by x pixels when moving). If the character (while still) was centered on the screen, you'd see half of one tile on the far right and half of another tile on the far left, so to combat this, the character was displayed off-center (in 1 of the 4 center tiles). VX chose the 544x416 resolution so that the player could be dead center on the screen and not cut off tiles along the edges. It still displayed at 640x480 resolution, resulting in pillarboxing and letterboxing because Enterbrain didn't want to scale up the image and end up with uneven pixel scaling.
640x352 could work in that it would have 4 pixels of letterboxing on the top and bottom (scaled up to whatever 16x9 display you have).
TL;DR:
The maximum resolution of the display is "full screen" as far as 2D games are concerned, but there are numerous considerations as to how you want your game to display, as outlined above. When you take out the output resolution as a factor, pixel scaling is no longer a concern, because it's not something you have control over.
