It kind of depends on which systems I'm backing up. And it would also depend on what you consider to be a viable backup. Many of my LANs would be in bad shape if, say, a tornado took out that office (which happened to one company I did a little work for a couple of years ago ... we found a computer in a field a week later and managed to get most of the data off the hard drive, but we were very lucky). I really need to think what might happen if some building burns down ...
Some of my LAN's use the built-in Windows Backup software to backup to a Samba share; one even just has each client box write to the next one in the office, theory being that no 2 hard drives should fail at the exact same time.
Some of my 'Nix boxen use tar(1) to write to a NFS mounted volume. ATM my webservers use a combination of PHP and Bourne scripts, combined with tar and some compression utility, (some use gzip, others bzip2) to write to another box on the LAN.
I have a few real small (windows) setups where I've just hacked together a batch file using xcopy, either across the network or from C:\ to D:\, for example. Handy for a standalone machine with 2 drives.
I'm currently most excited <?!> about rsync, which I think has been around a while; it's part of the Samba suite, a replacement for rcp(1). Running rsyncd on a 'Nix box is easy, and rsync is available for both 'Nix and Windows boxen. It's fast, easier to use than, say, xcopy, does its own logging, etc. I've not yet played around with compression, so currently I've got to have storage available for the clients at a 1:1 ratio, but I think that it supports some compression which might allow me to get more mileage from my server drive. I'd like to someday have most of the LANs using rsync, I think.
As for what others use, in 'Nix you've got cp, cpio, tar, dump, of which dump is supposed to be best, built in. AMANDA and Bacula are more extensive backup systems, and there are, I'm sure, others. I can't say what specific Linux distros may have as alternatives or whatnot...
On Win, you've lots of commercial stuff available, of course.