I've used many different methods, including the plastic milk crate. The crate is cheap, and it's very convenient, because it holds anything. Drop in whatever bag you have with you. You can go to the supermarket without a bag, they'll give you a bag for your stuff, and you can drop that in.

It's heavier than other methods, and it puts the weight high, which can affect handling of the bike, though not terribly.

Currently, I use panniers. They're more expensive, but they're a lot lighter than a crate. When I'm not carrying anything, the only excess weight I have is the rack. When I used a crate, it was inconvenient to remove the crate, so I was pedaling around both a rack and a crate.