A general bound that's sometimes useful is given by [Fernique's theorem](http://en.wikipedia.org/wiki/Fernique%27s_theorem).  It's a general fact about Gaussian measures on Banach spaces, but in this case it gives the following: there are constants $C, \epsilon > 0$ (depending on the dimension $n$) such that
$${\mathbf P} \left\{ \max_{t\in[0,2]} \|W(t)\|> x\right\}\leqslant C e^{-\epsilon x^2}.$$

You can find a proof in [these lecture notes of mine](http://www.unco.edu/NHS/mathsci/facstaff/Eldredge/7770/7770-lecture-notes.pdf).