I have a '98 Civic Hatchback and had the same problem as the caller with a '96 Civic Hatchback. I was able to track the water entry point to degraded seals around the brake lights. You can remove the panels behind the brake lights (on the inside of the car) and see if the water is coming in there. I replaced those seals and the problem was solved.
There’s already a recent thread about this, and I had the same issue with my Accord:
Check the rear quarter panel parking light/lens. I have a 1998 Ford Escort Wagon that had water leaking from that lens. The spare tire well filled up with water after every rain. You can’t see the leak unless you remove the interior quarter panel.
Is drilling a hole a good solution? I don’t think so. I guess I probably would probably try to fix the source of the leak and then sponge any remaining water out, rather than drill a hole in the wheel-well. I’d be concerned hot exhaust gases rising from the tailpipe would find it’s way into the passenger compartment if there was a hole in the underside of the car.
Many cars have drain holes in the trunk. However you do want to make sure that any holes you drill are not in an area where the road spray is going to come in.
For a 16 year old car, a drilled hole with a plug in it afterwards to seal it sounds like a real good solution.
I agree that the problem is the rubber gasket seals behind the taillight housings. They don’t exactly degrade, though, at least not in my case (I had a '98 Acura Integra hatchback – basically a rebadged Civic – with the same problem). The way the car was designed, all the rain runoff is directed down both sides of the hatch (under the hatch lip, but outside the weatherstripping) and right down on the top EDGES of these seals. Over time, dust and grit accumulates and works its way into the seals until a leak develops. Rather than replace the seals just to have the problem come back later, I cleaned them well and put a coating of silicone sealant on both sides before replacing the lenses. Yes, it’d be a mess to clean up should I have to replace the housing, but I didn’t plan on getting rear-ended 
better yet go buy a new foam gasket from honda and go get some heavy black rubber sheeting and trace new ones on the rubber and you wont need silicone