I seriously never understood why she's one of the more popular characters. Let's look at some facts:
Every single conversation with her in the first game is her whining. Oh we're the victims despite us attacking the geth first. Oh Shepard, I can't sleep because the ship is too quiet. Oh Shepard, I'm feeling sick. Oh Shepard, could you give me data you got so that I don't have to complete my own pilgrimage. She starts off the same in the second game as well. Oh Shepard, I've gotten my whole squad killed. Oh Shepard, I've gotten my whole squad killed... again! Bleh
She literally can't do anything on her own. First game: is stupid enough to think she can meet the shadow broker and gets attacked by two bit thugs and needs to be rescued. Second game, loses control of the squad she's supposedly in charge of and as a result, they all die. Later, during another mission she's in charge of she not only fails in her objective to figure out what is wrong with the sun, but once again gets her entire squad killed (unless Shepard manages to save Reegar). I won't hold her responsible for getting charged with treason, because that was her father's fault, but once again she needs to be rescued because she can't handle the situation on her own. Third game, she either dicks around doing nothing if Shepard didn't save her from getting exiled, or she fails to prevent a war because she's not assertive enough.
My favorite love interests (Liara or Miranda for male, Garrus for female) all ask for Shepard's help on occasion, but they are all capable of doing things on their own as well. Liara runs the Shadow Broker's empire, and saves Shepard's body from being given to the collectors. Miranda uncovers the secret behind Sanctuary, and of course brought Shepard back to life. Garrus wipes out whole gangs on Omega and organizes the Turian Military for war. What the hell has Tali ever done on her own?
My assumption is that she appeals to players with white Knight syndrome, because she constantly needs to be rescued, and because of her immune system is all delicate, manly male players can feel like they have to take care of her or some shit like that. Also, because you can't see her face, it can be whatever you want it to be, which to imaginative nerds like us I guess would be appealing.
Seriously, she annoys me more than the virmire survivors seem to annoy everyone else, because she has a personality, but it is just so god damn useless and annoying. Also, on a personal note, she sounds like my grouchy polish grandmother.