The OP said his boyfriend let him use his computer, no worry. Letting you use his computer definitely does not entitle you to delete or alter anything. Neither does it allow you to invade his privacy. Going into personal files, like photo galleries, unless expressly allowed, is breaking a trust in my opinion.
If a friend deleted files on my computer, I'd immediately pare my social list down by one. That's unforgivable.
My wife and I both have total, unrestricted access to each other's computers, but I avoid going into her personal stuff simply because I'd feel uncomfortable to do so. I'd never delete a file of hers.
Re:
@Sexyguy's original question: There are lot of reasons a person keeps files. Yeah, maybe he just forgot about them. Or maybe they bring back nice memories. Maybe they turn him on.
My first wife keeps nude and intimate photos of us in her bedside table, along with ones of her and her new hubby. . . I suppose for the same reason we kept them: they turned us on.