peanut's fantastic writeup does not necessarily apply if you're snowboarding in Europe, since we have button lifts as well as chair lifts (which are the type of lift referred to above). (If there are button lifts in the USA, too, I apologise, but I've never seen them there...) For those of you who've never seen one, a button lift consists of an extending pole attached at one end to an overhead cable leading up the mountain, and a disc on the other end that fits between your legs. The poles detach from the cable at the bottom of the lift; when you ski past, grabbing one, you also trip a switch with your shins/boots which engages the cable, allowing you to gracefully put the disc 'twixt your legs and be gently pulled up the mountain. (The pole is curved so as not to hurt your family jewels.)
That's all very well if you're a skier - you're facing forwards, and so you effectively sit on the disc. For boarders, they're an entirely different kettle of fish. Firstly, you're pulled up by your left (or right, if you're goofy) thigh, which is slightly blood-flow-inhibiting. Secondly, triggering the cable-engagement mechanism at the right time is tricky. Thirdly, most boarders remove their back foot, which impedes your balance: not good. Once you're at the top, you're pulled over a hump onto a downhill slope, at which point you must release the pole and slide off out of the way. Most beginners who have made it this far fall off at this point, which is not really a big deal, it's just annoying and occasionally painful.
You may notice that some boarders go up button lifts with both feet attached, which looks tricky, to say the least. In fact, it turns out that not removing your back foot makes the lift many orders of magnitude more managable. Not only is your balance improved, so you're less likely to tumble half-way up, but you're able to simply board away at the top. Fair enough, it's harder when you're just starting out, because you can't balance anyway, but it's definitely worth a try if you're having trouble getting the hang of the lifts.
mkb says we do have some similar things like t-bar and j-bar lifts. not very popular though. the one time i took a snowboarding lesson we were brought up by rope tow
T-bars and J-bars are horrible; I try to forget about them! Rope tows are easy, but slow, hence why they're used for beginners :p