CESM and COSMOS have been mentioned. A group in Japan has their own model, although I forget what it's called. If you really need a comprehensive list and a comparison, I'd recommend taking a look at any of the papers published in CMIP project. Our's (COSMOS) is in there and you can see where each model has its weaknesses.
Just as a clarification question, what sort of data are you looking for? Climate models differ a lot in what sort of things they do and don't include. Some have ice components, some have chemistry, some have aerosols and dust, etc etc...
As to the follow up question -- Meteorological and Climate models are extremely similar. In fact, you can run an Atmospheric simulation in "weather mode" and get (sortof) realistic weather patterns. The key difference, however, is the time step and length of model integration. Climate deals with long term averages of a system in both space and time, whereas weather is principally concerned with what may be happening over a week or two in a very local region. As an example, you wouldn't bother looking up the weather in Virginia if you lived in Florida.