Definition of lifespan (according to Wikipedia and this op):  The time between the first officially released game (any region), and the last officially released & licensed game (any region).

It should be noted that homebrew and unofficial games are still being developed for the majority of these consoles.

I used wikipedia game lists as my source, and sometimes checked their sources when things seemed odd (for example, Sega Gensis).  I was surprised by what I found in many cases.

2nd gen

Atari 2600: 13 years

3rd gen

NES: 11 years

Sega Master System:  11 years

4th gen

SNES: 10 years

Genesis: 13 years (14 years according to Wikipedia's source)

Turbo-Grafx 16: 7 years

Neo Geo: 14 years

5th gen 

Sega Saturn:  6 years

Nintendo 64: 5 years

PS1: 9 years

Atari Jaguar: 3 years

3DO: 3 years

6th gen 

Gamecube: 6 years

PS2: 8+ years (almost 9) and still counting.

Xbox: 8+ years and still counting.  (Most recent official game: Madden '09)

Dreamcast: 10+ years and still counting.  (Most recent official game: Wind and Water: Puzzle Battles)

After researching console lifepsans, a couple myths I held were dispelled:  Higher sales = longer lifespans.  Not true.  Better technology = longer lifespan.  Not true.  It seems people's devotion to a console as well as a company's inability to produce a worthy successor is most important.

PS3's 10 year lifespan doesn't sound ridiculous to me anymore - then again, neither does a 10+ year lifespan for Wii or 360.  It's a lot harder to predict than I first thought.  What happened with the 5th gen?  Why was it so much shorter than the 4th and the 6th?  And the big question: What's going to happen this gen?

WTF, Dreamcast was dead before the others even went on sale. It may have gotten a few releases since (in Japan, mostly) but Sega ceased production well before then and started making games for others consoles shortly after.

Also, try dividing that xbox number by 2 and you'll get the real one.

Yeah um Dreamcast went off shelves incredibly fast.

xbox is not still going, sorry.

 Dreamcast's most recent officially licensed game is "Wind and Water: Puzzle Battles" from November 2008.  Yes, it's in stores somewhere.  Dreamcast is still alive.  Same with Xbox, EA makes a new Madden ever year for that giant thing.

I find that definition too murky.  I mean, define "healthy number".  And when a manufacturer discontinues the console is sometimes several years after the last game.  Many people sound surprised about dreamcast, but it was still  being sold in stores alongside Wii.

If there are enough people still buying games to make new game development profitable, it's alive.  According to me and Wikipedia editors, anyway.  If you disagree,you might hurt some die-hard Neo Geo fan's feelings.

Well, when Sony says the PS3 is on a ten year plan, they mean they're going to support it for ten years. As in keep on manufacturing it and making games for it.

Not according to the OP's definition.  EA site for Madden 09 (XB) http://www.easports.com/madden09/fullsite/features.jsp?itemID=currgen

I don't believe Sony has defined "Lifespan".  But by your personal definition, Dreamcast still had an 8 year lifespan.

When was the last time Sega made a Dreamcast game? O_o

Sega Published "Under Defeat" in 2006, the game was on shelves next to Wii Sports.  So 8 year lifecycle, according to your definition.  It's still licensing games, so 10+ year lifecycle according to Wikipedia's definition.