Mice are ~30% similar genetically to humans, so a surprising amount of transfers. Rats are a bit more similar IIRC, but mice breed quicker so it's easier to do bigger studies...

Source: Used to work in mouse research on addiction (alcohol, cocaine, nicotine, etc).

Edit: This link gives even more specifics on the similarity: https://www.genome.gov/10001345 -- 30% is probably accurate, but in terms of function, it's even higher.