E.g. IGCM, HadCM3, HadGEM1, GFDL CM, CGCM, CCSM, CFS, and ECHAM.
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Yes. The biggest and broadest are the Palaeoclimate Modelling Intercomparison Projects (PMIP), which are the past-climate equivalent of the Climate Model Intercomparison Projects (CMIP).
The latest is PMIP3. It includes many of the same models that were used in CMIP5, as well as other models that are more focussed on representing past climates. The "overview" link on the PMIP3 page gives an indication of what the project covers, including experiments into the impacts of climate forcings, as well as benchmarking and comparison of models (e.g. quantitative and qualitative assessments of model performance over past climates).