This theory applies mostly to Rose and River since there weren't a whole lot of other characters that the Doctor was confirmed to be interested in aside from characters that only showed up for a single episode or two.
Anyway, I wondered why the Doctor would fall for two people with such radically different personalities (aside from the obvious reason that it's because they're both their respective creators' pets). Then it hit me, Rose and River both have something in common that's not incredibly obvious at first glance...
Notice how the 9th Doctor kind of liked Rose, but there wasn't any big huge thing going on between them until 10th arrived? Also, notice how the Doctor said in The Impossible Astronaut that he didn't entirely trust River, but he seems to have gotten over that by Let's Kill Hitler?
The reason behind both changes is because the Doctor found out about their connection to the TARDIS. Although he already showed signs of liking the both of them, The Doctor didn't fall for Rose until after she absorbed the heart of the TARDIS; likewise, the Doctor didn't completely fall for River until after he found out that she was conceived in the TARDIS.
And of course, as has been pointed out a few times over the course of the series, the TARDIS is the one woman that the Doctor truly loves, but he can never actually have, so he settles for the next best thing, which is people that have some kind of connection to her, biological or otherwise.