Favorite Blue Mage/Magic

This is really a half and half topic. You could really
only like the spells or you can only like the character.
I gotta go with Strago. The silly old man with a mohawk
was a welcomed addition to the party and I always loved
his Blue magic attacks as most of them were actually
useful. Second on the list would have been the Enemy-
Skill materia as it has been a life saver in almost
every playthrough of that game.
I never used Quistis, Quina's spells ranged from useful
to why the smurf the smurf do I have this spell plus Quina
would get really smurfing annoying most of the time.
Kimahri.... HAHAHAHA yeah smurf Kimahri. FFV was not a
really fun title and I couldn't appreciate the Blue Mage
Job in it.

Enemy Skill Materia is probably the most broken Blue Magic in the series barring XI. Largely cause it gives you the most diverse selection of elemental magic, some of the most broken defensive spells in the series, and very few "only good in rare occasions" spells.

Strago is pretty awesome and has a nice spell selection as well, but he gets most of his good spells late in the game and it's just too easy to sidestep Aero, Tsunami, and Quasar for his ultimate blue mage skill Grand Train. Other than that he's actually not too bad.

Quistis and Kimarhi would be okay if their skills weren't largely weak, mostly situational based spells, and tied to their Limit Breaks limiting their practicality.

Quina and the FFV Blue Mage Class are pretty badass but they are also both Guide Dang It. They are both pretty dominating but a lot of fans miss it, because they don't realize how many of their seemingly situational/useless spells are actually not so useless or situational, with a lot of the enemies and bosses very susceptible to some of the most devastating spells in the Blue Mages arsenal.

I agree it was fairly ridiculous for Square to became consumed by this theme they'd developed of attaching a character's "class" to their Limit attacks instead of their innate skills. This was not a horrible move in VII due to the fact that materia let you customize everyone to the point where they were pretty much every class simultaneously. It started to get more and more useless as the number in the title increased.

I've never played III, V, or VI. Enemy Skills were pretty entertaining and some skills are more useful that other materia (particularly as it doesn't affect your stats). I did use Quistis fairly often. I preferred her over Selphie and Rinoa until I learned how powerful Rinoa's Angelo limit could become (also before Irvine became available).
I personally couldn't stand having Quina in my party, but I went ahead and did IT'S sidequests anyway. Devouring enemies to learn skills was fairly amusing.
I honestly don't know how often I actually used Kimahri. I liked him more as a character.

I always love getting Beta way too early and destroying almost everything in FFVII. Trine too, later. In fact, FFVII is the only FF that has enemy skill that I actually bothered to partake in.

Enemy skill in FFVII is broken like others have said. But I always use it. :D

I love Quina for sentimental reasons, though his/her blue magic rocks as well. Frog Drop + Auto Life = Invincible.

Strago is good, but other characters in FFVI are much better. Similar with the FFV Blue Mage. Quistis and Kimahri are just ok.

My favorite though is the FFXI BLU. The best job in FFXI simply because it can perform any role. True, it can't outperform the specialists at those roles but I feel that makes it all the more interesting. I absolutely loved my bag of tricks and being able to pop out a needed spell for the situation when we didn't have enough of some other job. They also looked badass in their artifact armor.

Blue Mage is my favorite FF job. I hope they add it to FFXIV eventually and also every other FF game with the job system. :)

Are you saying Quistis's degenerator isnt broken?

White Wind (all FFs), Mighty Guard (all FFs), and Goblin Punch (FF5, where I'm usually at the same level as random encounters in the first world of the game) are the main ones that come to mind.

Blue Mages usually require a lot of work and effort. I love using Quina, but s/he's pretty much the only true Blue Mage I have ever used. Learning all of the skills in FFIX is fun.