I know that many designers work for LEGO but I was wondering if there was some 'Star Designers' that we should know by name. Of course, I would also like to know what they are famous for.
As there are more and more LEGO fans who become designers, some of them are already well known from the community and are very dedicated to fans, going to events and the like. They are actually just regular people and always have an amused look if you treat them like they have ascended to godhood status or something.
A few of them in no particular order:
We owe Mel some exlusive sets, including 3300003 LEGO Brand Retail Store, 3300001 Brickley and some (if not all, I'm not sure) Master Builder Academy sets. Mel also finalised the design of the first ever LEGO cuusoo set: 21101 Hayabusa
Jamie Berard, as cited in another answer
Markus is responsible for some huge Technic sets, including [8421 Mobile Crane] and the first Power Functions sets, 8275 Motorized Bulldozer
Also, LEGO has also issued sets designed by fans, which is the closest you can be of being a designer without being actually one. Note that some of the names on that list did eventually become full-fledged designers themselves.
To end, a little piece of trivia: the license plates on some vehicles usually bear the initials of the designer of the set. Have fun hunting them...
The most obvious one I guess is Erling Dideriksen, who was not only a Chief Designer on the LEGO City range, but also designed the element that many refer to as "The Erling Brick".
The LEGO Group have also started recently publishing videos of their designers talking about new sets they've worked on (especially the Lord of the Rings sets), which will bring more of their designers into the public eye.