The original requirements page on support.apple.com reads:
To use Mac OS X 10.4 Tiger, your Macintosh needs:
- A PowerPC G3, G4, or G5 processor
- Built-in FireWire
- At least 256 MB of RAM
- DVD drive (DVD-ROM), Combo (CD-RW/DVD-ROM) or SuperDrive (DVD-R) for installation
- At least 3 GB of free disk space; 4 GB if you install the XCode 2 Developer Tools
Back in the day when Tiger was new, the consensus - more or less - was that while you _can_ install Tiger on the very low end accepted machines, you'd probably not want to. While Apple says "256 MB" are the minimum, most users found that unbearable to use for anything exceeding TextEdit. 512 MB was considered the "actual" minimum requirement, although even with that, you wouldn't have much fun using iLife apps and Office if you've opened Safari and Mail at the same time. With 768 MB or 1 GB of RAM, it was a different _world_. With the main differences to Panther (Mac OS X 10.3.x) being Spotlight and Dashboard, users of older Macs were advised to stay with Panther, unless the applications you wanted to use specifically required you to use 10.4.
Of course nowadays, it looks a little different. If you want to use a new iPod, an iPhone or even only a newer version of iTunes in order to use its features, 10.4.11 is the _minimum_ requirement, so that upping a machine's RAM and installing Tiger can be very worth the expense.
Just keep in mind that buying Tiger (if you still can) as well as RAM is investing good money into old hardware. Depending on your needs, a more recent used machine can be a much better investment. intel Macs are around for quite a while now, which means that a Mac mini or a white MacBook with an intel processor can be found for not-all-that-much-more. That investment will allow the _newest_ software to run (even the forthcoming Mac OS X 10.6 Snow Leopard).