I once read a magazine article written by a woman who had (her only) one night stand in her final year at university, with another student. The condom split. She took emergency contraception and didn't worry too much about it. He seemed like a "nice boy" and not the sort to be carrying any nasty infections. A few years later she was in a relationship with another man and they wanted to stop using condoms, so they went to a sexual health clinic, got themselves tested and discovered she was HIV positive. If it can happen to middle class, educated people who are being responsible and using protection, it could happen to anyone. The most you can do to protect yourself is to make sure you and your partner are both tested for STIs before you start having sex, and realistically, how many people do that? And even if you do, you're still relying on your partner not to cheat.
Yes, it's very unlikely to happen, but how far you go to protect yourself really depends on which risks you're prepared to take and which risks you aren't. I didn't get tested for STIs before having sex with my ex-boyfriend (although I have been tested since) but I'd known him since I was 14 and knew exactly where he'd been. The older you get, the greater the risks will be, because you will both have had more partners.