Personally, I define a game series as any franchise of games including at least three titles. In order, I'd say my ten favorite game series are:

1.  Quest for Glory

2.  Metal Gear

3.  Final Fantasy

4.  Legacy of Kain

5.  Halo 

6.  Panzer Dragoon

7.  Monkey Island

8.  Warcraft

9.  The Soul fighting series (SoulCalibur, Soul Edge, etc.)

10. The Legend of Zelda 

Keep in mind, I made this list up off the top of my head so it is (as all lists should be) subject to change.