For pure utility, Liara is an excellent squad-mate, especially if you are playing a Soldier, Sentinel, or Infiltrator, as her Singularity power locks down enemies en masse, is very fast, and can easily be combined efficiently with Warp Ammo or Throw for serious damage. She may not be excellent at taking down defenses, but she's a crowd-control powerhouse.
However, my favorite squadmate is and will always be Garrus Vakarian. Overload takes out shields like no-one's business, Concussion Blast rips through barriers, and his armor-piercing ammo and sniper rifles/assault rifles make armor trivial. He's also fairly durable without having to rely on defensive powers like EDI and Vega.
There's also the fact that Garrus is the most interesting, dynamic, and nuanced squadmate in ANY of the three games. He gives both a serious look at the situation you're in, but isn't afraid to joke around. He goes through some of the worst experiences of any of the characters in the games, and still manages to stay focused on defeating the reapers. Hell, when I personally had all but given up hope, Garrus kept my spirits up and gave me the confidence to keep fighting. He made me believe that humanity, no, that the galaxy could win this war.
And, he's always stood by my Shepard. He joins up with you on the Citadel because taking down Saren is more important that following procedure. As soon as you come back in the second game, he's one of your first squadmates, and he's spent the last two years fighting the good fight on Omega. Then, for the third game he left you only to help out on Palavin, and immediately and without regrets joins your squad as soon as you meet up with him. My Shepard has been betrayed by the council, by Udina, Cerberus, and more. Old squadmates were either too busy or uninterested in helping Shepard out by the second game, and in the third all the survivors have their own issues and won't help either. To me, only Garrus has felt like a companion who would choose Shepard over anything or anyone else to stand by.
That's all.