I'll give another vote for Arcanum. I fell in love with the game from the moment that I half-jokingly said "Okay, let's make an orcish businessman" and then realized that the game was actually going to let me do that.

If I remember correctly you can reasign skills in TQ.

Definitely Arcanum. It's amazing the range on viable characters you can create. And it does chance how you play the game, what quests you can do, how you can do them.

Drakensang have some deep customisation

Oh shit you're right. It was actually part of the Gold version, which I have, when you get to (I forget the town) you are allowed for a price to redo your character design.

I guess it's been a while since I played that.

I remember I created a custom "vampire" class and gave the character some powers and a deadly allergy to sunlinght ^^ (OK, the char was quite useless in this situation, since shops were closed at night...)

I am not fixing at one character in this gaming world. I like each and every character in every version and also get the updated information about each game. It was a really wonderful path for entertainment.

I am going to second Mount and Blade. It's not the prettiest game in the world, but its customization options are good, the gameplay is excellent, the setting interesting, and it is one of the few games like Medieval II that can totally re-engross me after months of not playing.
Most people recommend starting out with War Band, because it has online and is much an expanded version of the first game, but if you're interested you might want to give the first one a shot just to appreciate it and to appreciate War Band more. I will admit, I only own the first and really can only recommend it.

Speaking of the devil, Wizardry 6/7 and 8 are on sale right now, I'm tempted for about the 3rd time in the last couple of months to get those games and give them another go, especially Dark Savant. During my first attempt more than 20 years ago, I tried to beat the game without switching classes which was rather unwise considering the gradually decreased usefulness of my basic characters which included a lizardman fighter and a mook psionic...good in the beginning but later on progressing the game with such characters came down to a crawl so I eventually gave up. If I ever play this again, I'll stick to sensible stuff like monks, or alchemists switched to ninjas later on. Now that I think of it, my alchemist was the most useful character in my noob party, at least as far as specialized magic users are concerned.

There's two things that keep me away from retrying Wizardry and that's the annoying stats rolling in the beginning, it can take forever to roll stats for an elite character. The other thing is time, if you only have let's say one hour you can do quite a lot in something like Diablo but in a game like Wizadry one hour is next to nothing.

Still, I absolutely recommend Wizardry (especially Wizardry 7) to anyone with an interest in character customization. Haven't seen anything like it in the last 20 years. There's games with even more options but not as well implemented into actual gameplay as in Wizardry.