The way I see it, when White plays 1. Nf3, he's saying "After you." since that excessively noncommittal move suggests he doesn't know what to do, and is waiting for me to do something committal. Therefore my response is to play 1...Nf6, which is like saying back, "No, after *you*...".
What do you play against the Reti (1.Nf3) and why?

I usually just try to transpose into QGD-type lines that happen after d4. I'm not a Sicilian player so don't particularly like ...c5 (or the diagonal problems that sometimes arise after a White kingside fianchetto). ...d5 is a little committal if White likes Kings Indian Attack lines.
That, and what Sqod said, motivates ...Nf6.

I play 1...Nc6, then if 2. e4 I get my KP game with 2...e5, but if 2. d4 I play 2...d5 when if 3. c4 I get my QGD Chigorin Defense. I also play 2...e5 against 2. g3 and 2. c4 (in the latter case reaching an English, and possibly in the former if White plays 3. c4)

Since I play 1...d6 against everything...1...d6!
If White plays 2. d4, then play tends to take on a KID or somesort, which is fine for me as it's part of my repertoire.
If White plays 2. c4, i'll try to get 2...e5 and if possible, 3...f5 in, aiming for the type of positions that Anthony Miles would approve of
http://www.365chess.com/game.php?gid=2195013

The advantage of 1 Nf3 is that it is white who is going to call the tune.Irrespective of black's reply White can steer the game where he wishes.Even in the case of 1..f5,white can opt to go for d3 rather than d4.If you don't like black to determine the opening which will be played,then 1Nf3 is your move.

1. Nf3 is interesting, I myself have played it in tournament games a few times with the goal of entering into a KIA, or reversed KID territory. I don't know a thing about 'Reti', as I would invariably play d3, e4 ideas, but I've found 1...d5 to be the most testing if White intends to play a KIA, keeping options open as to where the Bc8 will develop (f5 or g4)

You could look at it both ways I suppose. Black does have a large choice but he's usually restricted to some degree by what he plays vs 1.d4 - a thoughtless reply on move 1 could see him move ordered out of his normal defence if White plays a quick d4.
It should be noted that 1.Nf3 isn't the Reti in the same way that 1.e4 isn't the Ruy Lopez.

It should be noted that 1.Nf3 isn't the Reti in the same way that 1.e4 isn't the Ruy Lopez.
I noticed it depends on the author...
----------
(p. 492)
RETI OPENING
(1 N-KB3)
THE variable nature of this opening is indicated by the variety of names
under which it has been classified--Opening of the Future, Barcza
System, Catalan, King's Indian Reversed, Nimzowitsch Attack, Reti
Opening, Santasiere's Folly, and Zukertort Opening. Some of these
names have been dropped and many of the
distinct patterns, for instance the Catalan, are
now in separate sections. This chapter includes
only the Barcza System, Nimzowitsch Attack,
an Reti proper.
1 N-KB3 was recorded by Lopez in 1561,
Zukertort adopted it "incidentally" in 1845,
Reti moulded it into a distinct pattern after
World War I, and Barcza began the modern
trend towards the King's Indian Reversed.
The Reti is hypermodern, subtle, and flexible.
Reti himself said: "It directs pressure against the centre, prevents 1...
P-K4 and keeps open almost all the possibilities (of transposition)
for the first player." The pawn-structure is elastic. Few or no pawns
are placed on the fourth rank where they might obstruct their own
pieces or become objects of attack. Once Black commits himself in the
centre with ...P-Q4 then White directs his attack not at the weakened
K5 square, but at the target pawn itself by means of P-QB4, P-
KN3, and B-N2.
Evans, Larry, and Walter Korn. 1965. Modern Chess Openings, 10th Edition. New York: Pitman Publishing Corporation.
----------
Admittedly I believe more authors consider the Reti proper as 1. Nf3 d5, though, so personaly I use the name "Zukertort Opening" to mean only the move 1. Nf3.

You could look at it both ways I suppose. Black does have a large choice but he's usually restricted to some degree by what he plays vs 1.d4 - a thoughtless reply on move 1 could see him move ordered out of his normal defence if White plays a quick d4.
It should be noted that 1.Nf3 isn't the Reti in the same way that 1.e4 isn't the Ruy Lopez.
I believe you are wrong.
1.Nf3 has been labeled the Reti Opening in some Databases and some Databases label the move Zukertort Opening.
I believe both are considered correct.
Which makes you wrong.
You are right about 1 thing though.
1.e4 is not considered the Ruy Lopez.
However, 1.e4 is considered the Kings Pawn Opening.

I play d5 expecting some kind of queen's pawn opening eventually.
If I'm feeling tricky I do 1.Nf6 and I'll delay my center as much as theirs up to move 5 e.g. Nf6, g6, Bg7, 0-0.
In the 1...d5 cases I'm less familiar if they try to be tricky with d3 stuff, but those positions aren't dangerous I think, so it's not so important to know specific moves, just the ideas associated with the structures.

IMO, g3 seems like a pretty solid and flexible choice, the fianchetto can be delayed depending whether black needs to contest white staking the center.

1 Nf3 is a high quality first move,one of the very best(together with c4,d4,e4.)To say that white does not know what to do by playing 1 Nf3 is perhaps good for your morale if you believe it,however it has nothing to do with the reality.For starters, white may wish to avoid the Nimzo-Indian and prefer to play the white side of the Queen's Indian.Or, avoid the Budapest.Then ,white puts direct pressure on black by not allowing 1..e5.Whatever black plays,White will have control over the various transpositional possibilities.More brutal types of chess players may not fully appreciate the merits of 1Nf3 and may write it off as "passive" or "innocuous".Nevertheless,Nf3 is an excellent first move,not to be underestimated.

Reti - Lasker, New York 1924. Black plays London sys. like (d5, Nf6, c6, Bf5...). Look at this game - good formation against Reti.

1 Nf3 is a high quality first move,one of the very best(together with c4,d4,e4.)To say that white does not know what to do by playing 1 Nf3 is perhaps good for your morale if you believe it,however it has nothing to do with the reality.For starters, white may wish to avoid the Nimzo-Indian and prefer to play the white side of the Queen's Indian.Or, avoid the Budapest.Then ,white puts direct pressure on black by not allowing 1..e5.Whatever black plays,White will have control over the various transpositional possibilities.More brutal types of chess players may not fully appreciate the merits of 1Nf3 and may write it off as "passive" or "innocuous".Nevertheless,Nf3 is an excellent first move,not to be underestimated.
If you are playing to avoid the Budapest you have other worries than what to play on your first move. BTW I used to play the Budapest and I can attest to the fact that it's a smoldering pile of manure.

1 Nf3 is a high quality first move,one of the very best(together with c4,d4,e4.)To say that white does not know what to do by playing 1 Nf3 is perhaps good for your morale if you believe it,however it has nothing to do with the reality.For starters, white may wish to avoid the Nimzo-Indian and prefer to play the white side of the Queen's Indian.Or, avoid the Budapest.Then ,white puts direct pressure on black by not allowing 1..e5.Whatever black plays,White will have control over the various transpositional possibilities.More brutal types of chess players may not fully appreciate the merits of 1Nf3 and may write it off as "passive" or "innocuous".Nevertheless,Nf3 is an excellent first move,not to be underestimated.
If you are playing to avoid the Budapest you have other worries than what to play on your first move. BTW I used to play the Budapest and I can attest to the fact that it's a smoldering pile of manure.
Wow,you sound like an angry 2700 plus GM.For us lesser mortals,the Budapest deserves respect.

1 Nf3 is a high quality first move,one of the very best(together with c4,d4,e4.)To say that white does not know what to do by playing 1 Nf3 is perhaps good for your morale if you believe it,however it has nothing to do with the reality.For starters, white may wish to avoid the Nimzo-Indian and prefer to play the white side of the Queen's Indian.Or, avoid the Budapest.Then ,white puts direct pressure on black by not allowing 1..e5.Whatever black plays,White will have control over the various transpositional possibilities.More brutal types of chess players may not fully appreciate the merits of 1Nf3 and may write it off as "passive" or "innocuous".Nevertheless,Nf3 is an excellent first move,not to be underestimated.
If you are playing to avoid the Budapest you have other worries than what to play on your first move. BTW I used to play the Budapest and I can attest to the fact that it's a smoldering pile of manure.
Wow,you sound like an angry 2700 plus GM.For us lesser mortals,the Budapest deserves respect.
It doesn't take a 2700+ to realize the Budapest isn't that great. In fact, if you're strong enough to need to study openings, then you're strong enough that the Budapest isn't a great choice in slow OTB play.
Still when a below 2000 player calls the Budapest "a smoldering pile of manure" I am not sure I can agree...

Still when a below 2000 player calls the Budapest "a smoldering pile of manure" I am not sure I can agree...
- I played the Budapest as Black for 30-years so I speak from experience
- I am 2000+ at USCF correspondence dating back to the pre-engine mid-80's. It's right there in my profile, you might have looked.
I'm interested to know what you all play against the Reti and why.
I used to play 1...c5 hoping for a transposition to the Sicilian but this only happened once, most of the time, my Reti playing opponents play 2.c4. Thus I've decided to meet the Reti by playing 1...d5 and if 2.c4 then 2...d4 the so called "Reti Advance variation" that I noticed was scoring pretty well for Black. Which brings me to my other questions, does anyone play the Reti Advance variation (from either side), if so what do you think about it, and does anyone know of any books or videos that talk about the Reti Advance from the Black side? Also in the Reti Advance it looks to me as if Black gets more space out of the opening, so does this disprove what Kramnik said about the Stonewall Ducth being the only opening where Black gets more space?