I am wondering what are some of the most common parts that fail on Honda's?

 

the back wheel well! hah. thats typical honda rust. it really all depends on how well the car was maintained and how it was driven. check gaskets for leaks. most honda's water pumps are timing belt driven so if you're planning on a rebuild, replace both. a lot of civic motors are zero clearance between the pistons and the valves. sooo if you timing belt or water pump goes bad and the engine gets out of timing, you can clap a valve, no good.
but for the most part these little cars are really reliable and depending on the service record, have no problem exceeding 250-300,000 miles.
check engine and tranny mounts too.

 

Coil
Ignitor
pretty much anything distributor related
oil pan gasket
Front Wheel bearings
water pump if you dont replace it with the T-belt


Everything else is relatively typical deterioration once the car gets older, like cv boots and suspension bushings.

I always buy a spare coil and ignitor once my honda's turn 100,000mi. Learned that the hard way out in the middle of nowhere!