condoms may not protect you from...

genital warts.

How do they spread?

Genital warts are very contagious and are spread during oral, genital, or anal sex with an infected partner. About two-thirds of people who have sexual contact with a partner with genital warts will develop warts, usually within three months of contact.

In women, the warts occur on the outside and inside of the vagina, on the opening (cervix) to the womb (uterus), or around the anus. In men, genital warts are less common. If present, they usually are seen on the tip of the penis. They also may be found on the shaft of the penis, on the scrotum, or around the anus. Rarely, genital warts also can develop in the mouth or throat of a person who has had oral sex with an infected person.

Genital warts often occur in clusters and can be very tiny or can spread into large masses in the genital or anal area.

Source and for more information visit: Human Papillomavirus and Genital Warts National Institute of Allergy and Infectious Diseases, USA government

The warts may be removed but the virus will continue to stay in the body.

Condoms may not protect males or females as other exposed areas are not covered by it.

The virus that causes genital warts may lead to some cancers.

Actual photos of genital warts (not for the faint hearted):
Mediscan site
eMedicine site
Penile genital warts from US Navy Environmental Health Center
Anal genital warts from US Navy Environmental Health Center
Vulva genital warts from US Navy Environmental Health Center

My unsolicited advice, be careful when engaging in sexual activities with other people. It still good to not have casual sex or be monogamous.