You can use an external hard drive formatted as a Fat32 partition. The Xbox will only read up to 16 GB, though, I believe, so don't pay for a terabyte drive when it will only use 16GB max.
How Do I Use a USB Hard Drive With the Xbox 360? | Tech Tips - Salon.com
You can also purchase a new hard drive for the Xbox. That's what I did, upgraded to the 250GB hard drive. It's not very economical considering what Microsoft charges for them, but it's easy.
NOTE: I can't guarantee that you can save new map packs to an external hard drive. And I'm about 99% positive you can't moved already saved games to an external hard drive, but you can save future games to it.
EDIT: I just read that the recent dashboard update in November upped the space on external hard drives that the Xbox will read to 32GB. So replace what I said early about 16GB with 32GB.