Not a lot on a ride. I've used it to disassemble stuff I've bought for packing.
I have, on at least one occasion had a loose handlebar, and had to buy a multi-tool at a local hardware store to comfortably get home. Call it an assembly/build issue.
I did use the chain tool on my multi-tool once to fix a broken chain (9s, never 11s... yet). I'm now experimenting with Wippermann chains that come with very easy to use quick links, but I still would probably need the chain tool to clean up broken ends, should the need arise.
Tire levers are handy. And, a spoke wrench has come in handy a couple of times.
Anyway, I could probably get away with say a 5mm Allen wrench for stem bolts & etc, and leave the rest of the Allen wrenches home. Add the tire levers, spoke wrench, chain tool, and my Swiss Army knife, and I could deal with quite a bit.