Wanted to sort of voice my opinion on the subject here, little as it may matter. I've played a lot of RPGs in my time, and I always feel like some measure of romance (maybe not even involving the main character) gives the world some sort of texture it would not have otherwise. I've gone through entire games where the protgonist is a silent, unpredictable murderer and is revered by the people solely because he managed to hack his way towards the bad guy and kill him as well. At that point, it doesn't even feel like a role-playing game, more of a medieval slasher simulator (with gear! Wow!). Having the main character display an interest towards someone makes me feel like the game has an actual story. When it's a romantic interest, it puts me in the shoes of a character with personal goals, but maybe some depth of personality as well.
That all being said, poorly done relationships ruin the illusion. With an end goal like "sex" or "marriage" (a contemporary example could be Skyrim) the game effectively ends whatever interest you might have in that storyline. In the case of Skyrim, if you have played it you will understand how shallow a marriage system can feel. The "married" NPC is basically removed from the game, and there is almost no reason to pursue conversation with that character ever again. No respectful knight wants to spend a night with some wanting slattern, either. A few lines of dialogue leading into a meaningless, forgotten (and probably unseen) sex scene is a fast way to drop all emotional ties.
Frankly, the best of RPGs that included relationships made it a sort of challenge. Have a soft spot for that druid? Well, after she witnessed your spur-of-the-moment dog killing rampage, she might be less enticed to be on good terms with you. Want to get to know the captain of the town guard better? Your criminal record of breaking into houses might have something to say about that. If there is going to to romance or sex, please, please make it meaningful. Let it develop characters. Pester that elf until she gives you the time of day.