The maximum number of bitcoins that you can have in your wallet is a bit less than 13,364,954.77726004 BTC.
That limit increases by 25 BTC approximately every 10 minutes or so right now.
The rate of increase on the limit will be cut in half from 25 BTC to 12.5 BTC starting sometime late in the year 2016.
After that the increase on the limit will be cut in half again approximately every 4 years until the final limit maximizes at something less than 20,997,254.75406004 BTC
Wow really big numbers huh, tnx for the info
Of course, to reach those limits, you first have to convince everyone that has any bitcoins to send them all to you. Furthermore, you have to find all the lost private keys of those that have permanently lost access to their bitcoins. In many cases this can only be accomplished if you can discover cryptographic weaknesses in the SHA-256, RIPEMD-160 and ECDSA algorithms.