LÖVE

Forewarning: this is a rant. I've always had a hobbyist interest in video game design, dating way back to the days when I used to program in TI-BASIC over a decade ago. I kept up with the times as the years went on, always dabbling in different languages and engines but never really committing to anything. I discovered LOVE about 2ish years ago and haven't turned back! LOVE + Lua is such a fun language to play with. I think that's why most of us are here actually. But I realize I'm never going to accomplish much of anything until I become a competent artist.

Art: my nemesis, and the most important aspect of game design. "But certainly no more important than gameplay mechanics, or the story, or the audio, right? They're all equally as important!" I thought this too, but then I realized I wanted to produce something I wasn't somewhat ashamed of posting. I took a look at popular indie games, steam, ludum dare and other game jam produced games. Even if the art was extremely minimal/pixel based/color limited, it still had a strong aesthetic, a good sense or proportion, a pleasing color scheme, etc. Yes there are exceptions such as text adventures and ASCII roguelikes. How many of those games do you see winning ludum dare? Getting sold on steam? In the mobile world I see games getting judged almost exclusively on artwork. Just look at King's games: there's no gameplay innovation whatsoever, just really polished artwork and aesthetic design.

Stepping outside of LOVE for a second, there are a lot of tools (Game Maker, Construct, Stencyl to name a few) that help competent artists become game devs without needing to be competent programmers. How many tools are there that help competent programmers become game devs without needing to be competent artists? Uh....

So yeah, that's my rant for the day. I think I need to take a few months off programming, as much as I love it, and start doodling around with some drawings or something.

Sadly, I have to agree, this is a problem that I'm been struggling a long time, but there is a solution: find a friend that draws really good and make a team with him. It's very difficult to find a person who is good at programming and drawing. Although, there are games with bad graphics that have been really successful, like Minecraft.

The most important part is really just to have a unified aesthetic, a unified feel. That's more important than being good artwork.

You asked for "tools" helping programmers to draw. This is not excactly a tool, but I recommend this link:
http://2dgameartforprogrammers.blogspot.de/ A blog about how to create art, aimed at programmers. Good tutoirals on it! (Edit: I noticed he also started selling tutorials - click "older posts" for more free ones - there are quite a lot. Of course you can feel free to buy the new ones as well - I think the guy is definitely worth supporting. Just note that you don't have to pay for some great tutorials, most of them are still free.)

Also, I recommend to try out inkscape for making graphics. Off course, only with practive will you become a good artists, but inkscape makes it really easy to quickly create objects (which you can then export as .png files). And best of all, it makes it easy to create objects which all look alike (use black outlines and only a few, strong colours, for example). Animating in inkscape is also very simple: Just duplicate the object, then move some lines, duplicate again... and so on - and voila, you have your spritesheet.
Check out Bandana: we used only inkscape for the graphics and for the most part (some of the graphics on the blog are outdated), the graphics fit together very well, I think.

You could also try generating images in blender. It might help with shadows and the "similar" feeling for all images. Be careful however: Don't get lost in detail here - Blender has too many buttons you can push...
If trying to render world objects, you could enable "orthographic" or "isometric" camera settings.

Last advice I'll give might be the most important: My art teacher once said that when drawing, most of the time should actually be spent looking (I beleive he said around 80 or 90% of the time, actually). I totally agree with him there. There's so many people who take a glance at a person and then attempt to draw a human and fail horribly. Instead, for every line one draws, one should go back and look at the line in real life before drawing, after drawing it and when the connected lines have also been drawn, and when the picture is done. Game arts are very seldomly realistic, but it still applies here: When drawing a character, look at real humans or objects to see how the shadows work, how the colors work etc. and apply them to the cartoonish characters.

LuaWeaver nails it in the head.

Pixel art, vector, raster, 3D, cell shaded... they can all be gorgeous or awful. It is all about an unifying aesthetic.
And in all honesty, there is a lot of things that art and programming have in common.

Some quick, cheap and dirty tricks that help a lot:
-Stick to a single style. You wouldn't write a script with five different languages, don't mix 3D with pixel with vector art with ascii. It is gonna look like shit.
-If you are going to do pixel art, always do it in the same scale. Different sized pixels = big no no.
-If you need to scale pixel art, do so without any filtering nor anti-aliasing - this will preserve the pixel information.
-Avoid ultra thin lines and tiny details - they are more likely to become aliased noise than to actually contribute.
-Always work from global to local, think of it as closures: first you draw the basic idea of the background, then you draw the trees and only then you shade it.
-Reuse everything. Think like tilesets, feel free to reuse any art you do but *always* do it so it feels random and one cannot notice the patterns.
-Focus on the silhouette. Everything else is gravy, silhouettes are the fastest way to communicate visually - and are why dark, black and white games work just fine.
-Break rules from experience and with good reason.
"3D background with 2D characters gives great depth while not hampering progress, looks pretty good and works." is good reason.
"I got tired of 3D so I'll leave the backgrounds as they are but I'll make the characters 2D" is a shitty reason.