Ok, I could have swore this topic had been covered before, but couldn't find the thread.
The d20 core mechanic is fairly simple, but it's not the only one out there (obviously enough). A couple of other ones I know work as follow:
Percentile based: Stats and skills are given in XX% format. To succeed, you need to roll under the percentile value, which can be modified by outside circumstances.
GURPS uses a 3d6 method, again where you're trying to roll under the stat or skill to succeed. Generally the more you roll under your target, the better your success.
A different method is used by the White Wolf stable of games, where everything is d10 based. In these you add together the number of dice you have in a stat and skill, roll them all, and are aiming to get 7s or better for a success. The difficulty of the task determines the number of successes you need to achieve your objective.
A different one is the likes of L5Rs roll/keep system. In that, you have again a pool of d10s (stat + skill), but only get to keep so many of them. In this case, you add the totals of the dice up, and are aiming to reach or beat a particular number to succeed in your task. As an example, I have a dexterity of 2 and sword skill of 3, and am trying to hit an average target. I roll 5 d10s, and keep my best 2. If I get 15, I hit my target. If I don't, I miss. 7th Sea uses the same mechanic I believe, or something fairly close.
So yeah .. lots of different mechanics out there. Some don't even use dice. Castle Falkenstein, a steampunk game, uses cards (since gentlemen play at cards, and only those ruffians use dice in their games)