Oral sex is a big reason. Michael Douglas got tongue cancer* from HPV.

Actually it appears the 9-polyvalent HPV vaccine protects against multiple cancers but insurance won't pay for it once your outside the age window.

* originally he said "throat cancer" at the advice of his agent!

[edited: wityl pointed out I’d typed HSV for some reason]

You are thinking of HPV, HSV is herpes.

There is no vaccine, it doesn't cause cancer (that we know of, at least not like HPV), and spreads via skin contact on the genital area.

Since fluids are not required for HPV or HSV and it's present on the area that a condom won't cover, condoms aren't effective for either.

Yes it was a brain fart — fixed!

HSV-1 and -2 transmit through contact from skin location to skin. Including through asymptomatic shedding. Only sometimes is that location covered by a condom - in location and in timing.

See also: Wrestlers' "Herpes gladiatorum" which is just HSV-1. Which demonstrates how HSV-1 survives for transmission far more easily or broadly than just genital contact. Is there "HSV-2 gladiatorum"? Apparently it's usually HSV-1 but probably yes - neither HSV-1 or HSV-2 are really location specific.

I looked through the literature and it seems that condoms are quite effective at preventing HSV infection when used, especially from male to female (on the order of 99%), and less so for female to male (around 60-70%). I would suspect the reason for failure is behavioral. People probably don't apply the condom until after most of foreplay is over and HSV-2 can be transmitted during "outercourse".