I bought a Cannondal Trail 5 this spring and so far I have snapped four spokes in the rear tire. The guy at the bike shop said something about upgrading the rim if it continues. Is an upgrade the only thing that will prevent this from continuing, or is there a more economical alternative?

Could be a couple things going on here...either the wheel was not properly built to begin with or it's not strong enough for your riding. At this rate, I would guarantee it will continue. I would unlace the wheel, check the rim, and possibly rebuild into a new rim - a wheel that's properly built(for it's intended purpose) is critical to having a reliable wheel. The quickest/easiest option would be to replace the whole wheel.

I believe that as nc said it is a poor build of your wheels. But you have provided very little information to go by other than you are breaking spokes. It might help to know which side of rear wheel, where the breakage occurred (in middle, near nipple, at elbow), type of spoke (straight, butted, gauge), your weight and type of terrain you ride, spoke tensions (each side of wheel front & rear).

And I do not see how changing the rim would fix a spoke breaking problem unless it is a damages rim which results in uneven spoke tension to bring it into true.

I'm not to good with bike terminology, but I'll do my best to describe it.
They are breaking at the rim where they go through a collar. This is the back tire, not sure which side of the tire, or which type of spoke or any of that info. I weigh 280-290, I ride on sidewalks about half the time, and go trail riding the rest. This last break I heard it after hitting a bump on a trail, the one before it I set it down on the patio and POP another broken one. The other times it happened I didn't even notice until the breaks were making noise because the wheel was running out of round. As far as the specific info about what you asked the people at the bike shop have been fixing my bike so I don't really have that info.

Am a bit on the heavier side like you on a hard tail MTB (Gary Fisher Piranah)....
Bike shop replaced the rim with a stiffer rim.
Still break an ocaissional spoke, all on the rear (some at hub, some at rim). Ended up getting the tool to remove cassette to allow me to thread new spokes in.

With a broken spoke I noticed a couple of times that the wheel would run out of round, is that always the case with a broken spoke?

How old is the wheel. It may just need new spokes. I had the same problem a while back on a wheelset that didn't have that many miles on it. New drive side spokes fixed the issue.

Not even a year old yet. It's a 2011, but it was sitting on the shelf until I bought it in early 2012

spokes don't normally get much stress on the shelf.

Just one more question: is the spoke itself breaking where it threads into the spoke nipple or is part of the nipple staying with the end of the spoke and the 'head' of the nipple breaking off in the rim? If it is the latter, it's very possible that the wheel could have been laced with alloy nipples instead of brass. Alloy nipples do not stand up to severe service - - and I would put clydesdale rider in the 'severe service' category.

It has always been a clean break from the top of the nipple

So it's snapping off where the spoke meets the nipple and leaving the threaded part of the spoke inside the nipple?

Yes

If it were me, I'd replace the wheel with a hand built wheel from a custom builder, using stronger spokes and an upgraded rim designed for stressful use. I wouldn't re-use any of the spokes from the current wheel. So if you're replacing all the spokes and the rim, why not just start with a new, special built wheel. That should solve your problem.

as much as I would love to I don't have that kind of money for anything custom hand built