Here's my theory:
personally think there are 3. Consider:
Link #1
Ocarina of Time
Majora's Mask
New Gamecube game
Link #2
A Link to the Past (hereafter notated as LTTP)
Four Swords
Four Swords Adventures
Minish Cap
Oracle of Ages/Oracle of Seasons
Link's Awakening
the original game
Adventure of Link
Link #3
Wind Waker
Four Swords (Wind Waker Link version)
Now, my explanations for each Link:
Link #1: His first adventure is Ocarina of Time. Majora's Mask occurs some months later. The new GameCube game also seems to fall in this timeframe, because we have seen Link's faithul steed Epona in several screenshots. The new game may also include the famous "Imprisoning War" alluded to in LTTP.
Link #2: He is born 50/75/100 years after the events in Ocarina of Time/Majora's Mask. LTTP is his first adventure. After the events of LTTP, he travels the world in search of adventures. While we don't know exactly how many adventures he went on, some of those adventures were Four Swords/Four Swords Adventures, Minish Cap, and the Oracle games. Link's Awakening occurs on the way back to Hyrule. Upon return to Hyrule, Link discovers Ganon has somehow busted out of the Scared Realm and captured Zelda. The original game occurs here, and Adventure of Link occurs several years later
Link #3 is born hundreds of years later, when all of Hyrule is submerged under the sea, save for various islands. Wind Waker occurs