For the most part, they definitely are incentive for some people to take on extra challenges within games, and I see nothing wrong with that. Some people take them too seriously and put too much emphasis on them but who cares.
That said, I think that Achievements and Trophies are a great idea, but at an immature state right now. I had an idea that may well have been the next evolution of Achievements and Trophies: virtual items. As you know, Sony created the PlayStation Home platform as it's a virtual world where you make your own avatar, collect different clothing items, decorate your own virtual apartment, and play minigames within different 'Spaces' owned by different companies and developers to earn themed items and exclusive items.
There was a personal space called 'The Trophy Room'(developed, never released) where your Trophies were represented as virtual 'tangible' trophies (for example, a trophy from Loco Roco was a group of rendered LocoRoco characters). I think this would've been an exciting way to go about Achievements and Trophies. Get an Achievement on Halo 3, get a Spartan Helmet for your avatar to wear. Only problem for Microsoft with that business model would be A) the items would be earned, not sold slightly more development time to make the virtual rewards.
Anyway, I'm thinking of a reward system like in Bully, if you've ever played that game. You do a mission about... you beat a mission about boxing, you get boxing gloves put up in your room. You win the bike races, you get a bike racing trophy. Et cetera. I honestly feel like Motion Controls distracted from this development. (You have to go back and think about what Sony and Microsoft were working on before the Wii really REALLY proved its popularity to be more than a fad.)
Now, I'm not saying PS Home is perfect. Far from it. I'm just saying that Sony/Microsoft/Nintendo could've taken these reward items to the next level, if they had further persued the "virtual world hub" for their platforms (and they all have one. Xbox Live has that thing similar to PS Home(I remember it was supposed to be based on an Arcade and made use of New XBL Experience Avatars), Sony has PS Home, obviously, and I think it's fair to count Nintendo with it's Miis and Animal Crossing.
Whew.