Certainly he's exceptional in some areas, and probably exceptional in others. Hard to answer for sure, since other witchers aren't shown in action in the books. We have this passage from The Last Wish, the chapter called "The Voice of Reason 4":
‘Yes, Kaer Morhen. I underwent the usual mutation there, through the Trial of Grasses, and then hormones, herbs, viral infections. And then through them all again. And again, to the bitter end. Apparently, I took the changes unusually well; I was only ill briefly. I was considered to be an exceptionally resilient brat . . . and was chosen for more complicated experiments as a result. They were worse. Much worse. But, as you see, I survived. The only one to live out of all those chosen for further trials. My hair’s been white ever since. Total loss of pigmentation. A side-effect, as they say. A trifle.
See, only 4 of 10 boys trained in the witcher schools survive to become witchers... and I imagine not many survive long after that as well. Geralt is exceptional in that he's survived the Trial of Grasses, survived the more dangerous Trial of Grasses, and is still alive well into adulthood (he's around 50 at the time of the books).
He is also different because he is the son of a sorceress. While it is much a matter of opinion whether this gives him extra powers or not, there is this passage from chapter 2 of Blood of Elves:
Eskel emanated powerfully. More powerfully than Geralt.
Eskel, another witcher, emanates magic stronger than Geralt. But again, there's nothing else to base a comparison on.
Geralt also is implied to be the inventor and sole follower of the so-called "Witcher code". He claims he invented it himself in "Voice of Reason 4", and that no such thing exists in general. Certainly, Geralt has some stern moral principles which he tries to follow, and which sometimes go against the whole nature of witchering (e.g. not killing some beast, just because it's harmless).
Lastly, but most importantly, Geralt is famous. Geralt has done a few things here and there that make him very known, at least to some people, in no small part thanks to his friend Dandelion, who just can't keep his mouth shut.
He is known, firstly, for turning princess Adda from stryga to human. Given no one else was able to do this before him (and another witcher, Brehen, didn't manage to do this, even though he wanted to fight Geralt for this contract in "Season of Storms"), this also indicates he is very capable.
He is known as the Butcher of Blaviken, because he slew a infamous bandits led by Renfri, who were protected by ruler's letter of safe conduct. He killed all seven of them in swordfight, in the crowded market, because they threatened to kill all those unknowing people. However, they didn't actually attack.
Due to his white hair, a product of the advanced experiments conducted on him, he is known as the White Wolf. No other witcher in the books seems to have any title.
Dandelion made Geralt a character in (possibly more than) one of his ballads (from chapter 1 of Blood of Elves):
Your songs mention no names, but we know the witcher you sing of is no other than the famous Geralt of Rivia, and the enchantress for whom he burns with love is the equally famous Yennefer. And the Child Surprise, destined for the witcher and sworn to him from birth, is Cirilla, the unfortunate Princess of Cintra, the town destroyed by the Invaders. Am I right?