Ken Masters

Ken is Ryu's main rival.  Since children, the two have been trying to outdo each other and prove who is stronger.  So far, Ryu has the edge, but Ken has come close several times.

 

Sagat

Ever since his defeat in the first tournament, Sagat has wanted a shot at a rematch.  Sagat sees Ryu as a rival simply for the fact that Ryu was able to beat him.  Ryu sees Sagat as a rival because Ryu really had to dig in deep to defeat Sagat.

 

Akuma

Once Ryu discovered that there was something wrong with him (Satsu no Hadou), he went to find the person that might know the answers.  Akuma indeed had the answers, and Akuma wanted Ryu to unlock his full potential so that the two could finally see who is more powerful.  While Ryu has long given up the need to use Murderous Energy, the potential to become stronger then Akuma still remains, and for this reason, Akuma leaves Ryu alive so that they can have a final match.