assuming r and sigma are constant,
the solution should be
S_T = S_0 * exp( (r-1/2 sigma^2)T + sigma * W_T), where W_T is a standard brownian motion.

Check the wiki page on GBM at
http://en.wikipedia.org/wiki/Geometric_Brownian_motion

Sofa is correct.

You miss the Ito term, which is 0.5*sigma^2

The main point here is that, for common deterministic function, the quadratic variation is zero, since they are so-called "Smooth" function, but for Brown Motion, the quadratic variation is not zero, which means you need to include the second order term when you do the stochastic differentiation.

The right way to solve this SDE,is doing transform y=lnS, then apply Ito formula to y with respect to S.

It's done.