Visual Studio 2008 does not work with Team Foundation Server 2010 out of the box. Setting it up requires a few steps, here is what worked for me:
Assuming you already have VS2008 installed.
1) Install SP1 (optional, but may already be done): http://www.microsoft.com/en-us/download/details.aspx?id=10986
2) Install Visual Studio 2008 Team Explorer: http://www.microsoft.com/en-us/download/details.aspx?id=16338
3) Install SP1 (even if already installed from step 1). Source: http://blogs.msdn.com/b/jasonba/archive/2009/02/10/make-sure-you-reinstall-vs-2008-sp1-after-installing-team-explorer.aspx
4) Finally, install the VS Team System 2008 SP1 Forward Compatibility Update for TFS 2010: http://www.microsoft.com/en-us/download/details.aspx?id=10834
After much research and the above steps, I was finally able to connect to our TFS2010 server from VS 2008.
UPDATE: You can now just install a new GDR update for VS 2008 SP1 after the prerequisites have been installed.
Have a different method that worked for you? Please post a comment below letting us know.