I’ve worked on a couple of games in my free time now and each time I learn more about how to make the graphics look polished. Assuming that, dammit Jim, you’re a programmer, not an artist, here are some tips:
Choose a Theme
Come up with the concept of your game: is it going to be dark? Cheery? Avant-garde? Grungy? Sleek? This will inform all of the other choices you make. Make sure you can actually do the style you’re aiming for, though. For example, I love the “vintage grunge” look with lots of flourishes and distressed textures, but it takes me hours to make anything with that style, so I don’t.
Choosing a Palette
Having a color palette that you use throughout your game gets you 90% of the way to looking good. However, creating a nice palette is difficult. Fortunately, designers have this covered for you. Go to Kuler or Colour Lovers and browse the popular palettes. Choose something that fits your theme.
Even if you think you want everything in your game to be greenish, choose a palette with at least two contrasting colors (e.g., green and blue don’t count, green and purple do).
You’re only allowed to use these colors. In particular, do not use black or white, those “expert mode” colors. If the palette doesn’t have anything light enough or dark enough, use the Hue/Saturation/Brightness sliders adjust the Brightness slider until it’s a better shade. You’ll be amazed at how the darkest color starts reading as “black” and the lightest as “white.”
Note: make sure you’re allowed to use the palette, and of course credit it appropriately.
Rolling your own palette
If you want to create your own palette, check out the Final Boss Blues tutorial. It shows you how to create a nice combination of colors, even if you’re not artistically inclined.
Get a Nice Font
Google Fonts is the best source I’ve found. If you’re doing something not-for-web, you can download the font as a .woff and then use a converter to make it a “normal” .ttf (make sure you have rights to use it that way, yadda yadda).
By using these pre-built visual resources, I’ve found it’s a lot easier to make something that doesn’t look terrible. Good luck!