2d - How do you approach resolution independence in raster based graphics content?

Those games that are not fortunate enough to run on a locked platform spec, like handhelds, need to run across various resolution formats and aspect ratios.

In a 3D game you might have a HUD or menu GUI based on raster graphics, and in a 2D game you might have a bunch of quads which are vessels for sprites.

So my question is, how do you approach designing and operating content across various resolutions and aspect ratio? Let's assume you have a sprite character that is 300x400 pixels sprite and surrounded by a level made of tiles. On different resolutions/aspect ratios you'd see a different FOV altogether. Or if you have a HUD or a GUI menu, you'd want to keep some stuff at same positions and of same size relative to the screen. Yet, graphics source is raster bitmaps, not vector.

Obviously, problem has been addressed numerous times. I'm interested to hear abut various approaches that worked for you so far. Do you keep an arbitrary dimension agnostic 'pixel' unit that you magically transform into needed dimensions via formula based on res and aspect ratio or other approaches?

edit:

So, conclusion is to enumerate your aspect ratios. Lowest combination of aspect:resolution is the one you design important stuff into. A safe area if you will. Same aspect ratios, but higher resolutions are simple scaling issues. Art content is designed for highest resolution. Larger aspect ratios simply show more of level/FOV with information presented which is not critical as is the one in safe area. Something like in this image I made.

Answer

If your resolutions are similar to each other, you can just use the same art across all of them with maybe some downscaling at runtime for the smaller screens. If they differ by more than say a factor of 2x, you're going to need to author (or at least have an artist tweak) separate assets for the different resolutions.

With 2D, resolution has a huge affect on how you design images. A sprite that looks richly detailed and realistic at high-res will be muddy and indecipherable scaled down. Likewise, a sprite that's clean and sharp looking at low-res will look cheap and overly-simple at high-res.