Well I for one think "Star Trek: The Next Generation"
and "Star Trek: Deep Space Nine"
handled lots of romances well. I liked all of Picard's love interests except the one in "Insurrection"
(Vash, Nella, Kamala), Data's brief courtship of a crewwoman named Jenna, and the Riker/Troi stuff (especially when they got in a love triangle with Ro Laren in "Conundrum"
). The only one on TNG that I thought fell flat was Worf and Troi. Really forced and lame. I don't count Data and Tasha, that was mostly just a bad one episode gag, although Data mentioning it in "The Measure of a Man"
gave it a little more poignancy than it deserved.
On DS9, I thought Kassidy and Sisko and Kira/Odo were great together. Dax and Worf didn't work at first, but I finally found the relationship convincing and touching in "Change of Heart"
(a little late, but better late than never I guess). Bashir and Ezri being nervous like teenagers before finally getting together was cute too. I liked O'Brien and Keiko for what a realistic marriage with ups and downs it was, but didn't buy any of Kira's relationships with the Vedeks (I still can't tell them apart because they were both so bland to me). Those were about little more than lust, as far as I'm concerned.
I can't think of any romance on the original "Star Trek"
that was very memorable, other than Kirk and Edith Keeler. I'm a little surprised everyone's calling the Spock and Uhura thing in the new one a romance. Didn't really seem that way to me. I thought it was just her comforting him after his mother died, but maybe there's more between them that I didn't notice (I've only seen the movie once).