Advice for grad students: overcoming the feeling that you're an imposter (UPDATED)

Grad school can be daunting, especially for new grad students. It's a totally different experience than undergrad, and it's easy to feel like you don't belong, like you have no idea what you're doing, that you somehow fooled everyone to even get this far. In short, it's easy to feel like an imposter. Over at The Contemplative Mammoth, Jacquelyn Gill has a very nice post on how she got over her own "imposter syndrome". I particularly like the suggestion that acting as a mentor can be as helpful as receiving mentoring. Also the need to draw a line between generalized, ungrounded feelings of inadequacy, and specific respects in which you need to improve (a good adviser can help you draw this line). Some of her advice is less universal, but that's only natural--to an extent, everyone needs to find their own source of strength.

UPDATE: For a massive compilation of grad students and profs blogging about imposter syndrome, go here. If you've ever felt like an imposter, you are definitely not alone!

Did you ever feel like an imposter? How did you deal with it?