Support Vector Machines
The answer to your question is a bit tricky and here are good lecture notes to read to understand the various generalization error bounds. Let me try to summarize what's happening with SVMs and their generalization.  These PAC bounds are also found in "An Introduction to Support Vector Machines: And Other Kernel-Based Learning Methods" by 
Cristianini and John Shawe-Taylor.

Assuming a linear classifier correctly classifies all training examples (separable case), one bound (Vapnik '95 (I think)) on the generalization error of a linear classifier is (ignoring log factors):
$$
\epsilon = \tilde{O}\left(\frac{1}{n}\left( \frac{R^2}{\gamma^2} \right)\right),
$$
where $R$ is a bound on the size of the vectors, $n$ is the number of samples, and $\gamma$ is the margin, which is the distance to the support.  This bound says that the margin (the only quantity the learner has control over if the number of training examples are fixed), is an important quantity to maximize in SVM.

However, there is an intuition the margin is maximized in sparse solutions, and the sparseness of a solution is measured by the number of support vectors, so there is a relationship between the generalization bound and the quantity you're interested in.

Another relevant bound for any classifier (not just the linear case) is the following "compression bound" (Littlestone and Warmuth '86), which basically says that if a classifier gets $n$ examples right but can be obtained by training it on just $m$ examples then you can bound its generalization error by
$$
\epsilon \approx \frac{m \log n}{n-m}.
$$
Here, you can think of $m$ as the number of support vectors.  This directly relates the number of support vectors to the generalization error.

These two bounds help explain the interplay between the margins, the number of support vectors, and the generalization ability of an SVM (in the separable case).  In the non-separable case where you do not classify all training examples correctly, you get slack variables, slightly messier bounds, etc.