Which vaccines are damaged by freezing?
In order for a vaccine to work, antigens in the vaccine must maintain their shape and charge. Freezing a vaccine, particularly vaccines that contain aluminum, can cause antigens or other important constituents of the vaccine to aggregate. This may be what prevents them from working correctly, though we don't know for sure, and it may be something else about the freeze-thaw process. The main thing that we know, though, is that (typically in animal models, as in the last reference) for certain vaccines, if you allow them to freeze, they don't produce a sufficient immune response. 

You can look at this very large table of data about which vaccines are freeze stable and which are not.  There are a few patterns to this, as the OP seems to have noticed. 


Aluminum adjuvant: Any vaccine that uses an aluminum adjuvant (a chemical used to enhance the immune response) will be damaged by freezing. Polysaccharide vaccines and other purified or recombinant antigens are more likely to require an adjuvant. This is one of the reasons antigen only vaccines are more likely to be freeze sensitive. Some antigen only vaccines can be frozen themselves, and reconstituted with the adjuvant prior to administration (for example, some Meningitis polysaccharide and polysaccharide protein conjugate vaccines). 
Live attenuated vaccines: Almost all live attenuated vaccines are freeze stable (e.g., MMR, oral polio). The only ones that aren't, as far as I'm aware, are influenza vaccines: flumist and the live attenuated H1N1 influenza A vaccine. This may or may not just be a precaution, as I'm not aware of immunogenicity experiments that demonstrate freeze sensitivity.
Inactivated vaccines: Most killed or inactivated vaccines are sensitive to freezing. IPV is one of them. Rabies is an important counterexample. This is entirely speculation, but since many of these vaccines are formalin inactivated enveloped viruses or bacteria with cell membranes, freezing a perforated cell membrane may further damage it's antigenicity.


You can read about the basic principles of vaccination (e.g., how a vaccine works, what an adjuvant is, when you need it, etc) in Abbas Basic Immunology Chapter 8, and Murray Medical Microbiology Chapter 13.