Here, try this little circuit:
**broken link removed**
I just tested it, so I didn't just pull it out of my butt (or off the web somewhere). It works pretty well.
Not perfectly well, mind you: the problem is that the range within which you can adjust the brightness of an LED is fairly narrow, hence the top and bottom resistors. You could play with these values, with your particular setup, to arrive at a more pleasing adjustment action. But it is smooth, without any abrupt changes in brightness. The transistor should handle up to 8 or so "standard" (i.e., ~20mA) LEDs or so, or you can get a beefier transistor to control more.
Rled needs to be set to limit the current through your particular diodes. As others have stated, you should string them in series, not in parallel. (Or you can have series strings, each with its own resistor, in parallel.)