What Infectious Diseases can horses get that effect humans?
Eastern Equine Encephalytis, Western Equine Encephalytis, West Nile Virus, Rabies
For information on how common these are and their affects on humans, check out the Center for Disease Control website Eastern Equine Encephalitis | CDC Arbovirus CDC Fact Sheet: Western Equine Encephalitis - CDC Division of Vector-Borne Infectious Diseases (DVBID) CDC - Reported Arbovirus Cases in U.S. - CDC Division of Vector-Borne Infectious Diseases (DVBID) CDC: West Nile Virus - What You Need To Know CDC: West Nile Virus - Statistics, Surveillance, and Control > Case Count 2008 General Questions & Answers About Rabies | CDC Rabies Epidemiology | Rabies
For their affects on horses, EEE, WEE and WNV all are diseases that cause inflammation of brain and lead to neurological symptoms--weakness, lack of balance, lack of control of limbs, facial paralysis, etc. EEE has an 80% mortality rate. WEE has a 20%-50% mortality rate. WNV has a 20-40% mortality rate. All of these disease require a biting insect (typically a mosquito) to transmit them from one infected creature to another.
Rabies is also an encephalytic disease though it has a 100% mortality rate and can be directly transmitted from horses to humans.
There are vaccines against all of these viruses and they are considered "core vaccines"--meaning vaccines that all horses should get no matter how much or little contact they have with other horses because transmission is not via direct contact with other horses (or at least not ONLY through contact with other horses in the case of rabies).
The other "core vaccine" is tetanus. Tetanus cannot be transmitted from horse to human--it is a bacterial infection which is acquired via bacterial contamination of a wound.