Length, Width, Shape, Concave, Nose or tail, can all will be different with a skateboard. The skateboard you think of nowadays is typically a "popsicle shape" which generally has a symetrical nose and kicktail. These skateboards have this shape so that the board can be ridden both ways. There is no standard board size, they can range anywhere from a 7.5", 7.75", 8.0", 8.12", 8.25" and even bigger all the way up to 9.0" with some increments in between them. Smaller kids will ride smaller boards, and bigger guys will ride bigger boards.
The main thing is what you want to do with the board, street as mentioned earlier, or more transition and vert skating. While a smaller board will be used for the flip tricks, more stability on ramps can be obtained by riding a bigger board. Want something a little more directional? Don't be afraid of the shaped boards with the pointy nose or the square tail, those can feel very unique and will feel even better on transition with more leverage on the tail.