To me, rules are a necessary evil. Don't get me wrong; I do feel they are indeed necessary and I'm not advocating a completely freeform, lawless style of gaming. RPGs are games after all and games need rules. At the same time, it is my personal opinion and preference that rules serve to reinforce some element of the setting, genre, feel, and atmosphere of the game you're running but otherwise stay the heck out of the way.
I don't want to 'see' the rules too much. I want them to fade into the background as much as possible, except when they do something neat that makes me [or one of my players] say, "That's a clever way of handling that."
To that end...
I don't know that I have a game mechanic that 'inspires' my play.
I am not even entirely sure I know what that means. How would that work exactly? I feel inspired to create a character or scenario because the rules work a certain way?
Eww. Gross. I think I'm gonna be sick.
I really like the rules in Star Wars D6. I think the whole 'Wild Die', or Force Die as we call it, is a great idea. Coupled with the Force Points and Dice Pool it makes the action fast and exciting, whie still remaining fairly simple.
It doesn't exactly inspire me to play Star Wars though...I get inspired to play Star Wars and then I grab Star Wars D6 to run it because I like the way the system handles the setting.
The closet thing I can think of might be the magic system in Ars Magica. If I am feeling a Medieval Fantasy/Folklore vibe coming on I will read that game and its system and perhaps get some ideas for running a new campaign with it. But...I would have to feel that inclination first, before grabbing my Ars Magica book, so once again it isn't any mechanics that inspire play but rather ideas that lend themselves to certain mechanics and vice versa.
That's all I have one this one. My brain just doesn't work this way.