The redneck answer... until it begins to smell. The FDA Answer: 3 - 5 days.
In general, game meats can be treated much the same as other lean meats, assuming you cool them as quickly as possible after processing. Make sure to trim any fat from what you are planning to age as it will tend to become rancid more quickly than anything else. Also, if you wash your meat to remove hair or other debris, it should be eaten immediately as the moisture encourages decomposition.