I use a password vault program called "Keepass". I'm not necessarily endorsing it, although I'm happy with it.
I have one master password that is roughly 25 characters long, includes letter (upper & lower), numbers and spaces. Its essentially a phrase I'll remember. This password is used to gain access to my keepass database vault. Within the vault, I have all of my usernames and passwords, stored. When I setup a new account, I use keepass to generate a secure, random password, for each site.
The program then allows you to use two keyboard shortcuts to copy the username (CTRL-B) and password (CTRL-C). Or I can drag the user/password into the appropriate boxes on the program or website.
I additionally sync it with Windows Live Mesh, a cloud based storage provider. I chose mesh because I can easily access the files by logging into a website from any computer in the world (remember, I have a 25 char long password on the file, so even if someone hacks my password on mesh, they still have to break my master password - also my mesh password is easy enough to remember).
I now have a way to keep my password file in sync across my work, home and laptop computers, plus can access it on the road or at a friends house, if I don't have my laptop for some reason.
Because the passwords are random, I honestly couldn't tell you what my password was for any site, and if a person gains access to my flyertalk password, they won't be able to get into my bank account, trading accounts, FF...you get the idea.
Sometimes I miss the days of having a single easy to remember password across all sites, but after having my wife's email account hacked a while back, I'm convinced random passwords on all sites is the way to go.