I just started noticing a scraping noise(scrap....scrap....scrap..) that happens at all speeds but as soon as I touch the brakes it goes away. I have drums in the rear.

 

I would check your lug nuts. Make sure they are tight.

 

I just got back from a 200 mile trip. I'm pretty sure my wheels would have fallen off by then.

 

Sounds like you need to replace the shoes. When was the last time this was done?

 

I have never replaced the shoes and I have owned the car for 5 years.

 

Ya sounds like that should probably be done lol. Here is a DIY.
http://www.hondacivicforum.com/forum...acement-40934/

 

So I replaced the shoes, drums and all hardware. The sound went away and the car was fine for a few weeks. Now I have a new sound.... While I'm coming up to a stop light or stop sign and have the brakes pressed, I get a light clunk....clunk...clunk.... If I let off the brakes it goes away. I can only hear it when I'm about to stop(under a 5 MPH or so).

 

Hmm sounds to me like its time to get a quote from the scrap yard eh?

 

cheap drums? (under 20 bucks)

mine did that clunk clunk clunk....
I replaced EVERYTHING, shoes/drums/hardware/wheel cyclinders/EVERYTHING...

in my case it was cheap drums. I ordered a good set, that were $40 and put them on....solved the problem.

The cheap 18 dollar drums at advanced are garb.