I picked my 1993 Honda Civic DX up in 1998/1999 with ~74K miles on it. Still original clutch & trans, had to buy a new exhaust system about 2 years into owning it- old one rusted out. Removed the stock air intake/filter system and installed an after market cold air intake system, getting about 60 more miles out of it now than I was before. Also had to replace the right CV joint and boot after the boot ripped. Came with a lifetime guarantee, and it fell apart again this past winter (ran into ~8" of snow in that last big storm we had in MD), got it replaced with only the cost of labor.
Aside from the usual upkeep (spark plugs, oil, coolant flushes, etc), I've not had any problems with it except the exhaust and the right CV joint.
It has 158K on it now and still running fine.
If you are looking at older cars, 93 and later in the Civic model are pretty damn reliable. Just get one with low mileage.
Paid ~$6K for it.
-SW