www.logmein.com
I use that cross platform for remote access to my computers. They have a free version.
As for transferring files around, you have to keep in mind that transferring large amounts of data depends on how fast your Internet connection is, both where you are and where your computer is. Most Internet plans come with 1Mbit upload speeds (upload is what would be important if you were transferring files from your computer here to your computer there).
So lets say you have 5GB of music, a pretty low amount for most people. But even that would take 15-20 hours to transfer from your computer to wherever you are.
Transferring pictures and videos is going to have the same problem with the Internet connection wherever you are; I've seen hotels with speeds so slow it could be modem speed.
What you could do is basically make sure that when you are there there are 2 copies of everything.. Take a small netbook with a 160GB HDD and have your music backup on there, and then make copies of your photos and stuff from the memory cards onto it as well.. make sure you have enough memory cards to hold all the pics you want to take, then you'll always have 2 copies, on the memory card and on the netbook.
Then if one gets stolen you still have the other.
Or burn stuff to DVD and send it back to yourself?