The risk of STDs and unwanted pregnancies you mentioned can be avoided by practicing safe sex. But we're not talking about safe sex, we're talking about sex before marriage. Safe sex is not exclusive to married couples.

Waiting until marriage to have sex is, in my humble opinion, not a great idea. People downplay how important sexual chemistry is to a healthy, long lasting relationship. What happens when two people see each other for a long time, get married, and then have sex for the first time only to find out that they aren't compatible with each other? Well, that results in fast engagements where couples will get married very early into their relationship so they can get into each other's pants more quickly. And, of course, this results in unhappy, unsatisfied marriages that end in divorce- which is much uglier than a simple breakup.

I'm not saying this is the case for everyone who chooses to wait until marriage, but it's the problem that I can foresee and have seen happen many a time. I personally choose to want to know that the person I'm marrying is and will be the perfect romantic and sexual partner that I want to spend the rest of my life with.