I've just bought 2 TB HDD to be able to backup my desktop and laptop. I will have some files bigger then 4 GB, and I'll use it on at least 2 computers for backup. Is there any downside to format external drive to NTFS? Will I have problem if I use it on multiple computers?
Given that both machines are capable of reading NTFS drives then you shouldn't have any problems reading the data.
I've got an NTFS drive I had in my previous machine which I've put into a caddy to use as an extra backup and I've successfully used it on two machines.
Just make sure that you give "Everyone" full permission to the drive to be sure.
If you are going to use some smart software for the backup, do not use FAT (unless you never ever travel between timezones and there is no daylight saving time where you live).
NTFS properly stores the universal time when a file was modified and computes what that time means in your city to display it accordingly.
FAT simply stores a number, which is usually the local time (and I don't know how to make it store something else with Windows).
So, if you ever have to set you clock, files that were perfectly synchronized between FAT and NTFS will cause you terrible headache.
Some applications can be set to ignore timestamps that differ exactly by a few hours, but in the end you have trouble.