One of the biggest things I hear aspiring artists talk about is- individual artistic style, or the lack there of. I myself have only just reached what I feel comfortable calling "my style" so please take my thoughts with a grain of salt.
I believe that personal artistic style is a culmination of many different artistic influences that work in you, the melting pot, to create a consistent artistic vision that is slightly or hugely different from anyone else's. I want to put to rest the notion that any artist is operating wholly free from the artistic influences that surround him/her. We as artist enjoy looking at art, plane and simple, and there are artist's were admire more than others of course. These are our heros, our influencers without a doubt.
Seeing that artistic influences are a reality, there needs to be some advice on escaping plagiarism of style. My best advice in this area is to have as many influencers as possible, variety will help you for sure. Secondly don't doubt your own creativity, if it's easy for you to draw a hand one way and you like how it looks then just do it, and get better at it. I've heard alot of artists say that style is just something that finds you after awhile; keep producing work and you'll eventually get to a place you can call your own, I definitely agree with that.
A last, but large, bit of advice would be to make sure your influences are in the artistic world for the long haul, you probably don't want to get into the "trendy trench of death" a place littered with cute bubble letters, and owl drawings. You want your art to stand the test of time, so follow in the vein of timeless influencers.
The images above are from artists that I believe have had some significant, though silent, input in my own work. They are my influencers and inspirers. Check out the links to their respective blogs and online presences as you hover over their images.