Wings 1915

http://www.freeonlinegames.com/game/wings-1915

This is a game from FOG and you have to fly
your 2D plane and shoot down the enemy's.
It is a good game and very easy to play.
You use your mouse to control your plane
and shoot with the left click.

I couldn't find a video for this post, sorry.

86i

http://www.freeonlinegames.com/game/86i

This game is a full on 3D dogfight. You have to take out
enemy carriers and planes. I recommend you do the
tutorials before you start playing. This really helped
me.

F18 Hornet

http://www.freeonlinegames.com/game/f18-hornet

This game is from FOG and it uses the well known Australian
military strike plane, the F18 hornet. You have to fly this plane
and complete the various missions. I would advise that you do
the training first so you know how to work the game.

Stunt Pilot 2

http://www.freeonlinegames.com/game/stunt-pilot-2-san-francisco

This is an amazing game from FOG, it is one of their
most realistic games. You have to fly through lots of
hoops and try not to crash. You can use the arrow key
to guide you or you can  use your mouse.

Dog Fight

http://www.freeonlinegames.com/game/dog-fight

This is another great free game from FOG (free online games).
It is 2D but is great because its easy to play and has lots of different
levels each with different planes. Sometimes you have wing men and
sometimes you fight aces or bombers.
You fly using the arrow keys and shoot by pressing the space bar.