Yes you can. AIDS (the last stage of HIV infection, when the body is no longer able to fight infection and disesase) is transmitted through bodily fluids, so if you have sex with an HIV positive person and come into contact with their blood, semen (pre-cum included), vaginal fluids or rectal (i.e. the butt) fluids then you may become infected. Unprotected anal and vaginal sex are both leading causes of HIV transmission. It is even possible (though highly unlikely) to contract HIV through unprotected oral sex.
I'm not going to lecture you like your high school Phys Ed teacher and this isn't meant to be a scare campaign, but there are so many other STDs and STIs that are becoming increasingly more common. Do you really want to take that risk just for a little extra physical sensation? It's much less stressful and safer with casual sexual partners just to wrap up ya wanger before ya bang her/him/them and be sure to get regular sexual health tests done if you are sexually active - not only for your own health but for those that you get naked with.