Speed, Strength, Magic and Spirit are the only stats that can be raised by levelling up. The maximum is 50, 99, 99 and 50 respectively. However, it is not possible to a character to achieve maximum stats through the usual means.

Click here and scroll down to KADFC's Max Stats FAQ for more information. It may be useful, too, to take a look at SoftReset's Marcus/Eiko Bug Guide.