D6 Space is good, free pulp SFRPG. I actually have the hardbound edition of this game that I bought when it first came out. I had some fun playing in a D6 game before, so I was looking forward to the reissue. I imagined it would be just like the tried and true D6 Star Wars, only without all of the copyrighted material. Instead what I got was a game that crashed the Masterbook system right into the once enjoyably simple D6 rules. Ugh! So I put it on the shelf to gather dust. But now that it's been released as a free OGL game, I'm willing to cut it some slack. This game gives you a solid space opera RPG that you can run right out of the box, and when you add D6 Space Ships and D6 Aliens it covers all the bases.
Fuzion is a solid general purpose RPG engine that works great for space opera. Especially the older 4.4.3 rules, which includes different kinds of space suits, scanners, energy pistols, energy sabers, cyber hand blades, etc. It also has some cool dogfighting rules to handle those space furballs. Add the various plug-ins and you've got the whole genre covered. The Mekton plug-in gives you simple rules for building ships and vehicles; Mental Powers covers psionics; the Super Powers plug-in covers just about any weird mutant powers you can think of; and Martial Arts lets your your character have Venusian aikido. The only caveat is that Fuzion is more of a tool-kit than a finished rules set, so you'll need to do a little tweaking and adjusting, but that fits right in with the DIY theme of Jeff's post. For example, I'd reduce the number of characteristics to six or less and rewrite the skill list to add sf skills like sensors, zero-g, etc. And I'd beef up the Energy Sabre, which is too weak. Maybe something like this:
Tri-Stat is another good choice. It's a pretty simple game system to run, but it would require a little more work than the others to use for space opera. That's because the Tri-Stat dx rules are a generic version of the superhero game Silver Age Sentinels, and so they're focused more on a contemporary setting. But with a little DIY tinkering they would work, and they do include a space opera skill list.
There's a bunch more great free SFRPGS around, and you can find links to them under the "Free RPGs" label just to the right there, but these are the three I'd be most likely to use.