Katz's is probably the most famous, and still really wonderful. Anthony Bourdain loves it too, if you care what he thinks...

I want a Reuben so bad -- so for sure go to 2nd Ave, and then go to Katz's for a taste comparison. Maybe next week I'll get to Katz's if my work schedule becomes sane. Where else are you planning to eat?

If you are going to Katz's, make sure to take a side trip up Houston Street to Russ and Daughters. In fact, even if you ARE NOT going to Katz's, it's well worth a trip. Not a DELI, per se, but they carry a staggering array of beautiful smoked fish: several varieties of lox, herring, sable, etc. And sweets. It has been around for about 100 years, literally. They can make you a nice sandwich - take out only. I adore this place, but sadly live 3000 miles from it.
http://www.russanddaughters.com/

Katz Deli. Hands down.

Katz's system can be confusing for a first timer and look chaotic. You go in and grab a ticket out of the dispenser. There will be several countermen. There is not just one line. Pick out one guy and get in line for that specific guy.

Get out a dollar or two. When it's your turn, put the money into the cup in front of him. He'll ask you what you want and slice off a sample for you. Munch on that while you watch the artistry of him slicing and dicing.

After he's done with your order, hand him your ticket and he'll put down what you had. DON'T lose the ticket. Grab your food, find a seat and enjoy. You'll also get a bucket of pickles with your order. Oh, drinks are usually ordered in another line. Teaming up with another person is the best bet.

After you're done, you hand your ticket to the cashier on the way out for the final bill.

Sandwiches are huge and great!

Katz's...worth the second mortgage on your home.

Another vote for Katz's. Making me drool for that pastrami sammich I had a zillion years ago, shortly before I moved. I didn't know from Reubens back then either, and now that I know the love that is Reuben sammich, I'd come pretty close to selling my soul to have one of theirs.
I loved their minimalist/cafeteria cattle-call type M.O. So not pretentious as NY can be-and hopefully that hasn't changed.

seriously... Carnegie Deli!!!

Another vote for Carnegie Deli. Not so complicated either. But heck, why not go to both?

A surprise that the deli will be open on the Jewish sabbath (Friday sundown to Saturday sundown) but the web sites say that it's still kosher.

I don't think that you can go wrong with Katz's, Carnegie, or 2nd Ave.

Katz's Deli is the best!
It's at 205 East Houston Street on the corner of Ludlow Street.
http://www.katzdeli.com/

Incidentally, it's also right around the corner from the coolest bra shop in NYC, The Orchard Corset Center (157 Orchard St). The people there can just look your over and hand you the perfect size bra!
http://www.downtownexpress.com/de-164/findingtheperfectfit.html