Fav Consecutive Albums by An Artist

John Hiatt:
Bring the Family
Slow Turning
Stolen Moments

Fleetwood Mac (modern incarnation):
Fleetwood Mac
Rumors
Tusk

Grateful Dead:
Workingman's Dead
American Beauty
Live/Dead

Ooops...correction: Live/Dead precedes Workingman's and American Beauty.

Tumbleweed Connection
Madman Across The Water
Honky Chateau

Little Feat
Sailin' Shoes
Dixie Chicken
Feets Don't Fail Me Now
The Last Record Album

What Were Once Vices Are Now Habits
Stampede
Takin' It to the Streets
Livin' On The Fault Line

Court and Spark
The Hissing of Summer Lawns
Hejira
Don Juan's Reckless Daughter

Music From Big Pink
The Band 
Stage Fright

Skylarking
Oranges and Lemons
Nonsuch
Apple Venus Vol. 1

The Velvet Underground and Nico
White Light/White Heat
The Velvet Underground
Loaded

At Fillmore East
Eat a Peach
Brothers and Sisters

Fifth Dimension
Younger Than Yesterday
The Notorious Byrd Brothers
Sweetheart of the Rodeo

@hifijones - Way to dig up a 15 year old thread........ Since you brought it back, I'll offer a couple of good runs that I didn't see previously:

Rush 
2112
A Farewell to Kings
Hemispheres
Permanent Waves
Moving Pictures
Signals

Lucinda Williams
Lucinda Williams S/T
Sweet Old World
Car Wheels on a Gravel Road
Essence
World Without Tears

John Hiatt had a nice run in the late eighties with:

Bring The Family
Stolen Moments
Slow Turning.

He had done some great stuff earlier, and he's done some great stuff since - but those three are the rabbit passing through the snake.