No question in my mind: 5/11/1972 Rotterdam Civic Hall, Rotterdam, Netherlands Setlist is incredible. Dark Star, Dark Star, Dark Star.

Setlist:
Playing in the Band
Sugaree
Mr. Charlie
Black Throated Wind
Deal
Chinatown Shuffle
Mexicali Blues
China Cat Sunflower
I Know You Rider
Hurts Me Too
Beat it on Down the Line
Brown Eyed Women
Jack Straw
Big Railroad Blues
Casey Jones
Good Lovin'

Morning Dew
Me and My Uncle
Two Souls In Communion
El Paso
Tennessee Jed
Next Time You See Me
Dark Star
drums
Dark Star
Sugar Magnolia
Caution
Who Do You Love
Caution
Truckin'
Uncle John's Band
One More Saturday Night

No embed, but this will allow a listen:
http://www.archive.org/details/gd72-05-11.sbd.ashley-bertha.7364.sbefail.shnf

You really can't go wrong with any of the Europe '72 shows. Any of them.

Close second:
May 8, 1977, Barton Hall, Cornell University, Ithaca, NY

New Minglewood Blues
Loser
El Paso
They Love Each Other
Jack Straw
Deal
Lazy Lightnin'
Supplication
Brown Eyed Women
Mama Tried
Row Jimmy
Dancin' in the Streets

Scarlet Begonias
Fire on the Mountain
Estimated Prophet
St. Stephen
Not Fade Away
St. Stephen
Morning Dew
One More Saturday Night

For a listen:
http://www.archive.org/details/gd1977-05-08.sbd.cantor.sacks.266.shnf

I would also like to throw in my own personal favorite, as you know we all have them: my first Dead show. March 27, 1989, Atlanta, Georgia (The Omni). The first, but definitely not the last. That whole spring was magical.

http://www.dead.net/show/march-27-1989

Mississippi Half-Step
Walkin' Blues
Built to Last
We Can Run But We Can't Hide
Queen Jane Approximately
Candyman
Cassidy
Touch of Grey

Scarlet Begonias
Fire on the Mountain
Estimated Prophet
Eyes of the World
drums
The Wheel
I Need a Miracle
Standing on the Moon
Turn on Your Love Light
U.S. Blues

Had to slip that in. Good times (and great question).

The question should be what "tour" was the best, not individual show. Many shows had a truly magical "version" of a song that stands out above all others. For example, the "Eyes Of The World" at Raceway Park, NJ - 1977; or the "Scarlet/Fire" at the Worcester Centrum on 10/21/83; or the "Jam->Goin' Down The Road" at the Filmore East in '71; and of course those amazing acoustic shows in '80 that produced versions like the "Ripple" on the Reckoning CD. However, individual tours are an easier way to dig up the gems, either best individual shows or best versions of songs. Obviously, the Europe '72 tour is among the best of the best. The Spring of '87 was amazing, with rejuvenated life and energy back into the band that was not seen for a long time. The Spring and Summer of '89 was on fire, show after show. The Spring of '77 was amazing. And the fall of '83 was a really great sound for the band (that was the tour of the chimes, bells, and other calypso type percussion instruments). Those are the tours that for me, stand out above all others.

For a band that played 60,000 concerts this is no easy question. For the fan, the answer is of course the show that you went to, or stated otherwise, the show were you “got on the bus”. I believe the finest show is the closing of Winterland in 1978. New Year’s Grateful Dead shows were a staple of Bill Grahm events, and this one was for the ages. With the Blues Brothers Band opening, the Grateful Dead played three sets of awe-inspiring music. The third set being quite possibly the finest single set in all of Grateful Dead lore. Broadcast on local television (PBS), this was a bay area event that was eventually released on DVD. Enjoy a little footage of the Blues Brothers’ opening set with Elwood singing “Rubber Biscuit” here: http://www.youtube.com/watch?v=geeCTDL4yY4
Here is the setlist:
Winterland Arena, San Francisco, CA (12/31/78)

Sugar Magnolia
Scarlet Begonias
Fire on the Mountain
Me and My Uncle
Big River
Friend of the Devil
It's All Over Now
Stagger Lee
>From the Heart of Me
Sunshine Daydream

Samson and Delilah
Ramble on Rose
I Need a Miracle
Terrapin Station
Playin' in the Band
drums
Not Fade Away
Around and Around

Dark Star
The Other One
Dark Star
Wharf Rat
St. Stephen
Good Lovin'

Casey Jones
Johnny B. Goode

We Bid You Goodnight

Grateful Dead Live at Max Yasgur's Farm on August 16, 1969 (in other words, at Woodstock).
1. Saint Stephen
2. Mama Tried
3. High Time Tease
4. Tuning
5. Dark Star
6. High Time
7. Turn On Your Lovelight

I couldn't get them to embed, but here is a source for the music:

http://www.archive.org/details/gd69-08-16.sbd.cotsman.15205.sbeok.shnf

The short one.