How do I back up a bunch of OS X machines via TimeMachine without buying a bunch of Time Capsules?

A couple of options, in order of hack-ness:

• Install OS X Server ($50). Expensive, as you have to dedicate a mac to it, but you do get a lot of other stuff in the box.
• Install FreeNAS, which is appliance-like, and now supports Time Machine (see http://forums.freenas.org/archive/index.php/t-1157.html which indicates that as of August, support was in the nightly versions). Cheap, relatively painless to manage, and some options out there for commercial support to CYA.
• Install netatalk on a Linux or *BSD box; see http://www.tristanwaddington.com/2011/07/debian-time-machine-server-os-x-lion/ among other guides out there. This would be fine if you're already a comfortable unix sysadmin.

Whatever you do, however, your backups should be to redundant storage (this is doable for all the options above, although Apple's software RAID is generally looked down upon), and Time Machine backups should NOT be your only backup. FreeNAS has some backup capabilities, I believe - you can attach a big external USB drive and initiate a backup, and then send that drive off-site, for example. With a Mac OS X server, you could use Amanda (open source), Retrospect (shudder)...or...

Another option which I concede doesn't answer your exact question, but I think is highly relevant: Crashplan. Completely cross-platform (Mac, Windows, Linux, Solaris), they've got several different flavors, support inter-client backups (ie Bob can back up to Jane), multiple destinations, exclusion rules (for example, exclude everyone's MP3 collections). I use their enterprise version for 200+ seats and we love it. You lose the slick finder and installer integration (ie restore after fresh install from TM backup.)

Crashplan could also be used with one of the above solutions to provide your off-site backups with OS X server. For example, install the free Crashplan client, do the same with a system off-site, send the OS X server's backups to the off-site client, and set it to run only during non-business hours.

• Buy a NAS system supporting Time Machine. Many SOHO class devices do.
• Set up a system with MacOS Server and use the built-in TM feature.
• A Linux server with Netatalk installed should work as well. This is what is used internally by the aforementioned NAS devices in many cases.