I have several of them (and also a few PowerMac G5s) that my company was disposing of. Pretty much nobody is supporting OSX on PPC any more (for example, the last version of Firefox for it is 3.x). I notice that Linux is available for PPC, but how much software will run on it, since most Linux distros are for Intel?
Most Linux software is open-source and will compile fine on PPC; the exceptions are things that require direct use of the x86 instruction set or GPU stuff.
Yellow Dog maintains a distribution targeted towards PowerPC and IBM POWER architectures. The recent versions should still work on G5.
Note the amount of power these machines consume-- you could use one as a fileserver, or you could buy/build a tiny ShuttlePC and do the same thing faster with 1/10th the power bill and it pays for itself in 3 months.
Usually, once you include the power cost in the equation, using older hardware like that isn’t really useful. Unless you live in a situation where your power is “free”, or at least someone else pays for it.
What Blakeyrat said. The G5 wasn’t all that great when it was new, and it’s long been eclipsed by CPUs which are faster, run cooler, and consume way less power. The G5 was a last-ditch effort to keep PowerPC relevant in the desktop space, and it shows.
The appeal of the iMac was the all-in-one design. I don’t need a fileserver, and even if I did I wouldn’t use something like this. I’m thinking strictly in terms of clients (like something that my daughter can use to browse children’s websites) that would be on no more than a few hours a week.
I run a very old iMac (the Luxo style one) I retrieved from my father when he upgraded. I use it as a music server, and that is about it. The disk was upgraded some time ago, so holds my entire music collection with lossless compression, so it works out quite well. The power consumption issue is always worth watching. The iMac mostly used the Motorola PPC implementations, and these were pretty power frugal. The G5 on the other hand is far from frugal.
The G5 case is lovely, and if you ever need a sizeable chassis for anything is worth preserving. I’m seriously looking at using one as the container for bits of my home theatre build. You could use one as a very nice case for a modern motherboard and build up a server.
As to Firefox, there are builds of the more recent versions, TenFourFox provides what you want.
You can give one to me. 
An iMac like that can still run MS Office through the 2008 edition, which makes it a decent homework machine for a kid. Almost no one pushes Office to its limits, and a homework machine will get so little use that it won’t matter if the power consumption is bad.
You might also investigate whether it has value for remote access to other computers. For example, I ran my office for years with multiple computers connecting to one Windows XP computer using a little hack that allowed 5 simultaneous remote desktop connections. It didn’t really matter whether the connecting machine was Mac or PC, and hardware specs were irrelevant. The all-in-one design was nice to minimize wires on these “terminals.” Of course, setting all this up takes a little computer expertise (especially since that hack doesn’t work on Win 7 or 8, so you’d either need an XP server or a proper Windows Server OS with all of the licensing hassles those bring).
My Mac Mini G4 is pretty old and underpowered. But I still use it when I need to get Audible books into my iPod (iTunes is less dysfunctional than on a PC) or do some video editing with iMovie HD.
The vintage Safari browser is easily overwhelmed by modern Web sites. I guess word processing and spreadsheets are still a possibility for a non-power-user.
Well, if you have some potential uses in mind, lay 'em on us. In your OP you just asked “what is it good for?”
Keep in mind, the G5 will run every bit of software that was around when the G5 was being sold-- so there are undoubtedly tons of educational games and what-not out there, but it may be a little tricky to find.
As far as web browsers go, well, they have to talk to the outside world, so just ensure you have the most recent browser version possible, and if none of the available browsers have been updated in a couple years, understand that it’s likely you’ll have trouble browsing the web.
And definitely keep the power button OFF when you’re not using it. 