There are a number of ways to handle this. Some players LOVE rolling their own dice, and for them this is a key visceral experience in the game. This is why the player "honor" system is quite popular. It has been my experience, though, that the neutrinos start to spin the opposite directions when you do this: I once observed a Star Wars D20 game in which the median roll was 15 on d20. Many players cannot resist the temptation.
The other choice (the one I prefer) is simply to have the GM make all rolls. It is also a kind of "honor" system, since the players have to take the GM at his word. However, the GM is *allowed* to cheat, so if there is going to be dice-fudging I prefer it to come from the GM.
A third system is to use an online e-mail dice roller (there is a great one at www.irony.com). Whenever a character makes a test, the player logs onto the dice roller, makes the appropriate roll, and has the result e-mailed to him and the GM. The advantage is that it is a neutral, third-party determiner. The MAJOR disadvantage is that the game grinds to a halt as the GM specifies the roll, tells the player what modifiers to use, and then waits for the players to make the roll. Some gamers have sped-up this system a little by having players make a range of bulk rolls at the start of every action scene, and the GM just draws results from each result-list as needed.
Scottomir's LOTR Game Resources:
http://www.geocities.com/scott_metz/