I figured this would be the best place to ask this question, since the artists and layout designers hang out here.  Lately I've been working on a few small games I think I'll release for free.  Even though they're freebies, I still take some pride in them and would like them to look, if not thousands-of-dollars high quality, at least slightly professional.
  I was wondering if anybody had any suggestions on programs that can churn out documents with basic layout and motif stuff like borders and shading, or if anyone has suggestions on how to make a regular document look like more than plain words on a white background.

How large are your games? That influences the choice of software and work flow.

Noah,

What about sharing your games as they are and getting people interested by your materials first? You could maybe provide a very simple barebone WIP layout done with a word processing software like Open Office or Word, trying to make your best and connect to people with what you've already done. I'm maybe a bit too hopeful here but that could be a way to find connections with artists and people with layout skills, getting them hooked by your game first. I've often noticed that when I actually play my games with people, some chap pops up saying "you know, I'm a professional layout expert", or artist, or cook if your game involves cookies, or whatever.

Like you, I don't have much layout skills so I keep it as stupid and simple as possible, making the most of whatever my limited options are. Moreover, very simple layout options are often fittier and better looking than intricate so-called professional layouts. You can also buy very cheap layout templates, play a bit with the margins, headers and fonts in any word processing software and let us read your games sooner.