How It Works
The great thing about KeePass is that the database that stores your passwords is completely encrypted, so you don't have to worry about the file. That means you can put it on a USB drive. Since the program itself is so small and doesn't write anywhere except its own .ini file, you can put your passwords on a key drive and have them with you all the time. Even better, I use synchronization software to make sure that the database is always up to date on my home PC, my laptop, and any computer that I use at a client's location. (Sure they can see the file and have access to it...so what? It's encrypted!)
KeePass has tons of options, but I only use the basics. I log in with a master password and then I'm in business. Don't want to type passwords? No problem, you can copy username to the clipboard or the password, and paste it from there. KeePass will go out in a few seconds and delete it so you don't have to worry about it sitting out there. Even better, double clicking can fill in both for you. And yes, you can even setup shortcuts. For added security, you can set it to ask you for your master password again either every time, or on an interval. I set mine to ask me every time when I'm at a client site, and never after the first time when I'm at home.
Now, you're thinking, great, I can save passwords, but I still have to think of them. Nope, KeePass will randomly generate passwords for you using whatever length and character set you want. You don't even have to know what the password is, so it might well be impossible to crack.
If you need extra functionality or even tighter integration with your software, it has plug-ins that you can use as well.