A little bit of background first: there is no faster way to turn me off of a game than by saying "the combat sucks but otherwise it's great!" I remember not enjoying combat in Fallout 3 and Outcast, both of which throw quite a bit of it at the player. Especially in Fallout 3 and other Bethesda games, combat is something that exists in abundance, is rather necessary to progress through the game, and most of your character stats are about combat. You can tell me the game isn't about the combat all you want, but that holds no water when it exists in abundance within the game. Besides, if the story has war, conflict, and violence as central themes and plot elements, then there would be a bit of disconnect if I couldn't have fun participating in it, wouldn't there?

Now Gothic.

Gothic 2 in particular came to my attention when I heard a handful of people have claimed that Gothic 2 has a rather skillful combat system. I've heard that melee combat is pretty solid, that the system depends as much on player skill as character stats, and that sufficiently skillful player can even take on higher level enemies.

My question for you is: is the combat in Gothic 2 enjoyable? Is it something I would look forward to in the game? If Gothic 2 has good combat, then could I expect a similar experience in Gothic 1?

(Feel free to also say what other gameplay mechanics help hold up the game, as long as my original question is answered at some point. )

Tough one; I'm not you so I don't know if you will have fun or not. Gothic I and II have combat systems that if mastered, one can avoid most damage. However, the reason I never went out for sports is that they required one to practice - same with the combat system in I and II. I just mashed buttons and did OK (just OK) but I did have fun. Learning the system in detail was just too tedious, boring, time consuming, and required too much memory for me. III is another story as it was designed for the mouse. It mainly takes timing so one can do quite well (providing one uses the latest community patches) without the tedium and a few tricks like hit, turn run, turn, hit, repeat for many of the quicker beasts. You cannot do well at all just mashing buttons as the stun lock (even with the patches) will get you killed. You can never avoid damage near as well as in I and II (but, I was used to taking damage). All three can have you killed if one isn't careful at any time by any opponent especially early on and all three are unrestricted so you often run into things that are simply too powerful for you at the time. The combat system in one is quite old and not designed for the mouse at all (II takes it into consideration) - it is clunky. Much better if one has a gaming keyboard as the two-stroke command so often used can be combined into a single stroke.

All I can say is that I had fun in all three but found the combat system in I and II to be too tedious to master - it simply didn't matter as there are easy ways to heal.

Hand to Hand combat in gothic is all about rythm, and blocking against human opponents. Best played only with keyboard.
If you liked the combat-system of the first witcher, then give gothic a try.
To give you a kick in the right direction, here is the link for the english demo.

Yeah I wasn't able to find an english demo from that link.