Ryu is the basic bread and butter Streetfighter character. He has no major weaknesses and has the tools to deal with almost any situation. With the addition of his fake fireball feint move, your options with his famous fireball traps are endless.
Basics.
When throwing fireballs, mix the speeds up. Throw a light one or two as they are hard to jump straight up over, then drop a fast one in to throw people.
Ryu's Dragon Punch is an excellent anti-air, but a jumping middle punch gives two hits, and if you jump again quickly and unleash another - you can get three hits and massive damage.
Ryu has arguably the best standing overhead move in the game. Pressing forwards and middle punch while standing will make him hop forwards with a downwards punch. It hits twice and must be blocked high, so jump in with a kick sweep combo, then repeat but instead of the sweep throw the overhead out and catch people out every time.
His super may not seem amazing - a hadouken fireball on steroids, but it doesn't leave you vulnerable and it can be thrown from the far edge of the screen. It can be combo'd in for more hits and in a fireball throwing contest - is an instant trump card. It will snuff any other fireball and go on to hit your opponent.