Yes. Having unprotected sex with many partners increases your risk of getting HIV because it increases your chances of coming into contact with someone who has HIV. It also increases your risk of getting other sexually transmitted diseases (like herpes, gonorrhea, chlamydia, venereal warts, or syphilis). Having an STD, in turn, can make you more likely to get HIV.
However, having unprotected sex with anyone who has HIV, or whose HIV status you do not know, puts you at risk. So, even a person who has unprotected sex with just one partner can still get HIV if that partner was infected prior to having sex or becomes infected during the relationship.