I'm feeling wicked smart right now.
Our apartment has an ancient gas-gas stove (for those who haven't been obsessing over old stoves, that's a gas oven with a gas heater built into it, which they don't make in the states anymore). The oven stopped lighting sometime in the last few years but the old tenant never mentioned it to us, new tenant noticed it recently.
I could see that the pilot light was lit, and it got bigger when you turned the oven on as it should. But the safety valve wasn't getting the signal that it should open up and send gas to the burner. I thought I'd have to replace some parts (thermocouple, maybe safety valve).
But I fixed it by simply shop-vac'ing clean the dirty pilot light assembly! Turns out whatever was in there must have been preventing the pilot light from getting the thermocouple hot enough to signal the safety valve to open up.
Total cost to replace the stove with a new one would have been about $800, getting a repair person out to look at the thing would have probably cost at least $120 for the service call.
My Total cost: $0
Win!