Now, while it's true that RP doesn't guarantee the correct answer 100% of the time, it does guarantee that the failure probability is bounded for every instance of the problem. This allows us to efficiently amplify the probability of having the correct answer to be arbitrarily close to 1. So in practice, RP and co-RP (and for that matter, BPP as well) are basically P for most practical purposes.
Comments: Paper is withdrawn because a counterexample was found to Theorem 1
I'm not entirely sure if approximate algorithms are included in RP.
Although I suppose you could consider RP to be an approximate algorithm for a decision problem, although it doesn't guarantee it's close it just guarantees it's right at least x% of the time.
In contrast, a randomized algorithm in RP is one which is guaranteed to be able to tell you whether there is no solution with 100% accuracy, but, if it says a solution exists, it is only correct to within some probability p.  A good example here is the Miller-Rabin primality test. [2,3]
: Incidentally, although it's a little obscure, I did once manage to dig up the original paper that contained the elements of this algorithm. It was quite readable, IIRC. I may see if I can find it to post later.