I fell for Liara T'Soni (Mass Effect) pretty hard. Sure she's attractive as hell but it's more than that. She starts out as an intelligent, capable but slightly awkward and naive character but matures quickly, as one would have to do when suddenly faced with the threat of galactic extermination. Despite her new-found confidence, though, she never truly loses that sweet and gentle side of her character; she tries to hide it and be all business but that just makes the moment her mask slips and she smiles all that more sweeter.
Sticking with the Mass Effect trilogy, I'm going to be mega-predictable here and also say that Garrus is a legend. Confident, dependable, loyal and with a keen sense of humour to boot. This is offset nicely with a slight awkwardness around women and a tendency to carry the weight of the world on his shoulders at times. During my first playthrough of ME2 I cocked-up and got him killed in the final mission. My reaction was to shove my chair abruptly back from my PC desk, clamp a hand over my mouth in shock and I actually shed a (manly) tear or two...
Garrus Vakarian might just be the greatest video game character created, in my own, humble opinion.
Stepping away from Mass Effect and into another favourite realm of mine, Fallout, it was hard to find a character I really "bonded" with from Fallout 3 and New Vegas. I think it's because there are so many NPC's in the two games that personalities are not as distinct and fleshed-out...it's kinda hard to put my finger on but very few seem to have that elusive, mysterious factor that the ME characters have. That said, I do have to give a shout-out to Three Dog, someone who is entertaining, honest, decent and doing his best to keep people's chins up in a horrible environment - a post-apocalyptic wasteland. Even when playing as a complete bastard, I always fix GNR's relay because Fallout 3 without Three Dog and the excellent music he plays, just wouldn't be the same.
Skyrim suffers a similar problem in that there are not as many eminently likeable characters and the vast number of NPC's results in way too many with the same kind of personality. Even companions don't really grow and evolve as they do in other games, which is why in Skyrim and Fallout, I generally go it alone.
In GTA 4, I had a lot of time for Little Jacob as he was one of the few characters who wasn't annoying, whiney or just downright un-likeable. He always struck me a good bloke who did right by his friends and always has their back in a fight. I'm struggling to think of a character I really got attached to in GTA 5...