WindowsIdentity exposes a Groups property which returns a collection of IdentityReferences for the groups that a particular user is a member of. However, if you look closely, you'll find that these returned groups won't necessarily include all of the groups that the user is a member of.
Under the covers, WindowsIdentity populates the groups collection by querying Windows for information on the groups that the user token is a member of. However, before returning this list, the Groups property filters out some of the returned groups.
Specifically, any groups which were on the token for deny-only will not be returned in the Groups collection. Similarly, a group which is the SE_GROUP_LOGON_ID will not be returned.
Generally, this is exactly the behavior you want. For instance, if your application is going allow a specific action because the user is a member of a group, you don't want to allow it if the user is a member of the group for deny-only.
If you want to retrieve all of the groups however, there's not an easy built-in way for you to do this. Instead, you'll have to P/Invoke to the GetTokenInformation API to retrieve the groups yourself.
It can be interesting to dump out the groups that specific users are part of -- here's a simple little snippet of code that does just that. (And uses some of those fancy new C# 3.0 features to display them grouped by domain):