I currently own a Droid 1, which I use on a day to day basis. (yes I haven't upgraded yet). I was running a custom rom, Cyanogenmod 7.1, which is based on Android 2.3.7. Even though I was clocked at 800 MHz, I found the phone extremely slow. I was really frustrated with it, and felt like throwing it against a wall most of the time. I was trying to find a solution to make it fast again. I deleted all my apps, but that wasn't very effective. I used Android task killers and tried several ways to free up ram, but the phone still lagged a lot. After doing extensive research online on a faster rom, I learned about a rom called Liquid Smooth, which is also based on Android 2.3.7, which has several Cyanogenmod features on it. Anyways, I read that Liquid Smooth was like the fastest rom for the Droid 1and several people in forums praised it for giving new life to their Droids. I went ahead and downloaded that rom, and it gave my Droid 1 new life. With this rom, I was able to clock my Droid to 1 GHz and my Droid 1 ran incredibly fast. No more lags, no more force closes, and no more crashing apps. Even with several apps installed on my Droid, its still smooth. The quadrant benchmark went up to around 1200, from a previous 800. In fact, this rom made my Droid the fastest it has ever been. Even though I'm running at 1 GHz, the battery life is still good.
So getting to the point, if you have an old Android phone that is very slow, there are several thing you can try.
For non-rooted users, try to have fewer apps installed and keep fewer apps/widgets on the launch screen. Maybe experiment with different launchers, such as LauncherPro on the Android Market. Uninstall misbehaving apps. These weren't that effective for me, but it might work for you. Maybe reformat your phone, if all is in vain.
Now if you are rooted, there are several thing you can do to speed up your phone, such as overclocking it or flashing different roms. Some roms are sluggish, while others are super fast. Uninstall Bloatware, and using advanced settings on custom roms are also other ways to make your old Android phone faster.
What I recommend doing is what made the most effective difference for me, which was flashing the a high performing custom rom, which for me is the Liquid Smooth rom. Research different roms for your phone and see which ones gives the best performance. To Droid 1 owners, if Cyanogenmod or the rom you are on isn't good enough, maybe give Liquid Smooth a try (http://liquidsmoothroms.com/). To users of other phones, research it. There are tons of great custom roms out there.
Of course, some of these tips are easier than the other. No matter who you are, there will be some sort of tweak here and there to help you out. Let me know what you did on the comments. Feel free to ask any questions too.