Mountain Biking - Specialized Rockhopper Comp Disc 29 - Switching shifters?

I have an 09 Specialized Rockhopper Comp Disc 29 that I got back in June. I've been riding it as much as I can but all the other bikes I've owned have had the Shimano Rapidfire style shifters - where you use the thumb and index finger to shift up and down.

The new bike, has "SRAM X-4, 8-speed trigger" - which uses the thumb for shifting up and down. I've tried to get used to it, but I just can't - I prefer the other style. The rear derailleur is a "SRAM X-5, med. cage".

I've been looking at replacing shifters, but can't seem to find which SRAM shifter I can use to replace the ones I have - if SRAM does in fact make one like I'm after.

Can someone point me in the right direction?

You will need to replace both derailer and shifter. Your current X.5 derailer requires a SRAM shifter using the 1:1 pull ratio, and to my knowledge that means a thumb-thumb shifter.

I'd look into Shimano's new SLX line. An SLX rear derailer and a set of SLX shifters would get you the thumb-finger shifting you are after. You might be able to find the parts on eBay for $100 or so.

So I can use a front SLX shifter with my current "Shimano Altus, 34.9mm clamp, top swing" derailleur? If I'm replacing everything else, I might as well do the front derailleur while I'm at it.

Looks like I'd be getting the following:

Shift levers: SL-M660
Rear derailleur: RD-M662-SGS
Front derailleur: FD-M660 (or FD-M660-E).

However I noticed my rear cassette is only 8 - the RD-M662-SGS is 9. I'd need the CS-HG80 cassette sprocket as well. Will that fit on the back? Are the proper mounting holes available for derailleurs on the frame?

That derailluer will work fine. You don't need to get more speeds, though you can. The 9 speed derailleur WILL work with the 8 speed cassette. I'm running a 9 speed xt on a 7 speed.

Sorry. I missed your statement about having an 8-speed in your original post. Don't buy the SLX shifters. They will not work for an 8-speed rear-end. My mistake in suggesting them.

Could I still install a CS-HG80 onto my rear wheel in place of the existing sprocket?

Sure, but isn't the HG-80 a 9-speed cassette? You'll need to install a 9-speed shifter and a RD that can handle 9 speeds as well, and a 9-speed chain.
IMHO, going to 9sp from 8sp doesn't get you anything really useful in mountain biking, and the 8sp stuff is more robust and cheaper. Your choice, though.

You could try some twist shifters.