Short answer is - yes you can.
Not only STD's. I suspect that I caught tonsilitis that way once.
Gonorrhoea, syphilis, hepatitis, herpes and warts are all possible. (probably others too that I haven't thought of.)
HIV is said to be possible, but it is very hard to get a straight answer on how much risk there is.
Any wounds in your mouth (ulcers, bleeding gums, bitten tongue etc.) increase your risk a lot. They may also increase the risk to your partner if you have a blood-contact disease like HIV or HepC.
You can also get crabs in your beard. (I'm serious.)
Check out the Centers for Disease Control site for official medical information. Google is your friend.


