Perhaps your old Mac has Firewire? If so, you can use an external hard drive, or if you are going to a new Mac (hint hint) then you might be able to use Mac to Mac transfer over Firewire, although I am not sure if this is supported pre OS X.
If you don't have firewire, and no external drives of any sort, you are stuck with either (a) internal network, or (b) use of one of those Web based storage mechanisms like .Mac or box.net, where you can stash your stuff up on the web and then pull it down to the new machine. Typically however, this will be painfully slow, since most DSL high speed internet links are much slower on the uplink than the downlink.