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The first Gundam series produced was Mobile Suit Gundam in 1979. This is the first part of the Universal Century time line.

There are many alternative universes to Universal Century, though most of them only last one or two seasons at most. So, you could just start watching a newer alternate universe Gundam without missing the direct backstory.

Seed, followed by Seed Destiny, is a separate universe though you'll recognize a lot of elements if you know the previous universe.

Gundam 00 is a different universe from both of them. Again, many elements of previous Gundams are present and re-imagined, so if you know of them already, it's a bit of a bonus.

There's a listing of the series and what order they came out here:

http://en.wikipedia.org/wiki/Gundam#Animated.2Fliv...