LÖVE

I think that this is actually a great question and I look forward to seeing the answers.

Personally, I think it's just whatever is easiest for whatever you're building. Of the last four games I've made (all game jam games) the sprites were 128x128, 50x50, 32x32 and 50x50 pixels, respectively. BUT they were all consistent within each game which probably the most important thing. It's really annoying to have to adjust scaling and offsets for each individual image if they are not consistent.

For sprite sheets/atlases, 1024x1024 or even 2048x2048 (or around those dimensions) are perfectly fine, i'd think.
As for the individual elements, that'd be up to you, but i do think they're usually powers of two sized as well.

Also, as an example, older pokemon games, like blue, for example, has the sprites taller than the tiles, so it's not necessarily a thing to have every object be the same size; though the most-behind ones should be, for convenience.

Try not to exceed 4096 when creating spritesheets or backgrounds because you may stumbled with devices that have an upper limit which sucks, still 4096 should be a safe bet considering LÖVE 0.10.2 works with OpenGL 2.1 and up

To the size, as everyone said, go with whatever size you want for your game, an ultra realistic/artistic game doesn't use same size as a pixel game... Same goes with colors and aspects (top view, rpg, platformer...)