I collected Beige G3s for a while. I think I have about 8 now, desktops and towers. I had worked out that the logic boards were about the right size that I could suspend them from thick wire rails in the drawers of a filing cabinet.
Since they are ATX, I figured I could run several boards off one higher rated PSU (The Apple PSUs had feeble wattage ratings, a 600W PSU could probably run 10 of these guys without displays and netbooting would remove the need for individual HDs)

The whole project was inspired by Xgrid, which would just about run on these machines if you maxxed them up to 10.2.8, the minimum OS for the original Xgrid client software.

I eventually abandoned the project since I figured I could spend a few hundred on PSUs, ethernet cards, and the various required splitters, cables, interconnects, fans and various other sundries and I would end up with a 3 drawer filing cabinet with a maximum theoretical computing power equivalent to maybe a low end PowerMac G5 or a couple of gameboys gaffer taped together. Only this power would only be available to software or scripts that I could write or find to run over Xgrid, so it wasn't about to run Quake or anything.

Ultimately, it would be less powerful/useful/versatile than an iPhone, while costing more money, taking up about ten thousand times the space and drawing enough juice to send a Delorean 30 years into the past.

They are a good form factor to mod with. Fairly small, several off the shelf parts you can swap out (think tiny ATX PSUs from rack mount servers for example) plenty of upgrades available. Be aware that modding one is a labour of love, not a sound financial investment. You can stick a 1GHz G4 and a radeon 9200 in it but it isn't going to play guitar hero or much else less than a few years old. HD playback is also not likely - I tried to get a Cube doing this, the bus and RAM are too slow, and the Beige G3 is 30% slower.

A reasonably cool mod would be to gut an old CRT TV. Fit the G3 and a flat panel, a pile of storage, maybe with a RAID card and a faster network card. That would be a nice stealth mod, since CRTs are cheap and heavy and no thief worth his salt would dream of taking one in this day and age.