Just got done helping a few people out with their outrageously slow Droids, so I figured I'd just start a thread for it.
1. Clear Cache: Often times, different applications will store temporary information to make things easier. This can be anything from stored images to make pages load faster, recent search terms, history, etc. Generally, this information isn't vital to the operation of an app, therefore, it should be deleted if needed. Settings > Applications > Manage Applications > Options > Filter: ALL > Options > Sort by size. This will give you a list of applications based on how much space they're taking up. Click any given application and it should give you the option to clear the cache. Normally, this won't make a monumental difference, but it's a step in the right direction.
2. Uninstall Unneeded Applications That Constantly Run: The biggest example of this is your antivirus program (if you have one). In my opinion, it's a waste of space and memory. Android phones are Linux-based, so you don't need to be as cautious as some people are on their Windows machines. (For more info on this, you can refer to Oh Thank Goodness, Someone Made an Antivirus App For Android - antivirus - Gizmodo. Just don't be an idiot with the internet and don't open suspicious emails and you'll be fine. You'd be surprised how many people complain about outrageously slow phones because they think they need an antivirus. Some other things that have the potential to slow you down (or waste battery life) are Google Latitude, Maps, and things like that.
3.Widgets: Another great way to speed up your android phone is to minimize widget use. Apps/widgets that enable more than one screen tend to cause the phone do slow down and/or lag for a lot of people. A decent alternative to having more than one screen is to just make folders. For instance, I have an entire folder for my apps and another for my tools. I found that the facebook app sometimes even slows down my phone. This wasn't a big loss because I could always just open the facebook app and check that. A good rule of thumb is if you don't need it, get rid of it. If you do need it, explore alternatives.
TIP: Don't waste your time with programs that specialize in closing running programs. It's not needed. Android phones (maybe not all of them, but at least the Droid) will close apps when they need more memory. As far as battery life goes, you don't need to worry about renegade apps either. From what I understand, when you escape from a certain app, it doesn't keep running, but instead, it makes a little note of what you were doing so when you start the app back up, it reads the note, and jumps back to where you were, using a very limited amount of memory.
That's all I have for now. If you have any questions or suggestions, feel free to comment below or shoot me a pm.