I did it with a Elf Fighter/Wizard.
Elves have a LOT of racial perks and while Fighter/Wizard takes forever to level up, it is still survivable, and if specialised as an archer it can be exceptionally deadly being also an Elf.
Finally the lack of armor can be remedied somewhat with a natural high dex and 1st level spell "Armor" is long-lasting and provides a good defense.
Basically with this class you want a few defensives spells and maybe a few crowd-control spells to keep the enemy blocked while you murder them from afar with bow and arrows.
The Fighter's THAC0 and hitpoints, coupled with the Wizard's spell list makes this a versatile and survivable character, although it will take longer to level up and thus needs a bit more care than with a single-classed character

**SPOILERS**

For BG1 all you need to do is spam wand of monster summoning, Sarovok will go down, but will take a while.
Also, for a leg up early in game you can do the export/import trick, you can leave Candlekeep as a lvl 7, but it will take quite a few "restarts". I wasn't able to kill Gorion though, so just leave him be, the other guy to watch out for is a mage walking around the interior gates of the library that casts a death spell. The mage at the inn is easily dispatched by walking down/up the stairs making him waste his spells. Do the quests, then when you are sure you can take on the guards/mages start by whipping out the town. Kinda fun at first. When you can't get past a certain point just export your character and then import him into a new game.
BG2 is a bit different, it fixed a lot of the "game exploits", but you can use the Export/import trick if you play the multi LAN game. Right before you take a hit by that dream sequence that makes you choose a stat to lower, the demon asks you which essence would you like for him to take. This also works in the final stage where you have to take the tears of bhaal, if your a paladin you may become a "fallen paladin" and you will NOT be able to use the Holy Avenger taken from Firkraag, this is done if you choose an evil path in the Tears of Bhaal tests, thus you use the import/export trick to get around this, this will not work in the single player part of the game, although in multiplayer you don't need to have someone join your game. Also, its fun making your own group, sans a slot or two, so you can complete some of the beneficial story paths.
Killing dragons are easy if you spam Cloudkill just enough so it lowers the dragon's hitpoins but not enough for the dragon to heal itself, then you go in for the kill and you will take the dragon out. This is tricky since you have to be just at the right distance to cast without the fog of war revealing the dragon. Once you learn Gate, you can kill a dragon without ever seeing it. This doesn't really work with the Shadow Dragon, but will work with other dragons, except the White Dragon she will go after you, but you can just use the staircase to just cast spells, she is too big to get a shot at you if you keep your troops back and just fire projectile spells.
Have Fun!

Okay, I am bad about letting minor spoilers out (such as I may have about BG2 romances) every once in a while, but your post needs a HUGE spoiler warning at the top of it. True, it is an 11 year old game, but you gave away some largish plot/story points with that post.

I

It looks like the OP has played the game before, or he would not have asked about beating the game without using a fighter.

For me, personally, the game has more variations in storyline than just the main quest. I've had to replay the entire game several times to catch everything.

I don't think I revealed much of the storyline with what I wrote, I didn't mention who Firkraag was, nor did I mention how you got to those dream sequences. I also didn't mention where the dragons were but merely how to beat them easily if one is inclined to do so.

I mentioned an easy way to beat Sarovok, but I did not mention how you got to Sarovok. My tips are easily done be it whatever race/class you may be.

I mentioned being a paladin merely because the path you choose can nerf your paladin if your not careful. As to what the tears of bhaal are, where you are at that point in the game, why you came to be there, I didn't reveal any of that.

The OP has played the game, but other people reading the thread may have not.

No, you didn't give away anything about the main plot, but you gave away lots of little things. Things that would have made the game less fun for me had *I* known them in advance the first time I played through the series. That is the reason I asked you to edit your post and put a spoiler warning at the top. Is that really too much to ask? It doesn't invalidate any of your points, it is just common courtesy.

lol, k mate, I concede your point.

Thanks. I edited my spoiler reasons out of the previous post, as well.