I like musicals and plays and Cirque du Soleil. The broadway shows I've seen (as far as I can recall) are listed below.  Favorites are in bold.

42nd Street
Annie
Annie Get Your Gun
Annie Warbucks
Anything Goes
Avenue Q
Blood Brothers
Brigadoon
Bring in 'da Noise, Bring in 'da Funk
Bye Bye Birdie
Cabaret
Camelot
Carousel
Cats
Chess
Chicago
A Chorus Line
Cinderella
Damn Yankees
Evita
Falsettos
Fiddler on the Roof
Five Guys Named Moe
Forever Plaid
The Full Monty
A Funny Thing Happened on the Way to the Forum
Godspell
Grease
Guys and Dolls
Hair
Hello Dolly
Here's Love
HMS Pinafore
How To Succeed In Business
Into the Woods
Jekyll and Hyde
Jelly's Last Jam
Jesus Christ Superstar
Joseph and the Amazing Technicolor Dreamcoat
The King and I
La Cage Aux Folles
Les Miserables
Little Shop of Horrors
Merry Widow
Miss Saigon
Music Man
My Fair Lady
Oklahoma
Oliver
Paint Your Wagon
The Phantom of the Opera
Pippin
Pump Boys and Dinettes
Ragtime
Rent
Rocky Horror Picture Show
Sayonara
Seussical: The Musical
Side Show
Singing in the Rain
Smokey Joe's Cafe
The Sound of Music
South Pacific
Spamalot
State Fair
Stomp
Sunday in the Park with George
Sunset Boulevard
Tommy
West Side Story
Wicked
Will Rogers Follies