Why do players often play Nf3 while Fianchettoing their bishop on the kingside?

 It seems counterintuitive to me. A knight on f3 will not only block their bishop and a pawn on f2 blocking the eventual push, but also very rarely has any good moves at their usual position.

A knight on e2 however supports both f4 and d4 gaining significant control and can eventually jump to f4, d4 or c3.

The knight will be revealed usually creating another threat, but it also takes control of the center more so than if it was closer to the back.... 

The Nf3 doesn't "block" a Bg2 in any significant way; its power is revealed as soon as the N moves. The main reason you see Nf3 more often than Ne2 after g3 & Bg2 is the N is usually best placed there. See for reference the Black side of the King's Indian, White in the fianchetto variations of the KID, Benoni, Catalan, etc.

In general, you need more of a reason to post the N at e2. f3 is its most natural & usually most effective post, as it controls more center squares & more squares on the opponent's side of the board.

Thanks for the answers.

I'm still a bit sceptic about this move. A knight on f3 usually doesn't have many good squares and I automatically consider moving it a second time a loss of a tempo. Also when it is on f3 it cannot just move away to support f4, usually making almost all tries of taking the centre virtually impossible.

A knight on f3 seems to be good only when you want to attack the King.

 I don't think you want to "attack" the king if you are Fianchettoing on the kingside.

A knight very rarely can jump into d4, d5 and g5, unless in the opening, because the black pieces would be happy to try to control these squares, both with minor pieces and pawns, and if that happens, your bishop is usually locked with the knight, unless you are jumping on d2 (which can be often hard to do!).

 "I don't think you should randomly give away pieces even tho' you aren't sure if you are getting them back"

"Shows me games with gambits, a knight sacrifice and a positional queen sacrifice"

The threat of a discovered attack with any knight move is often more valuable than the bishop having direct sight over the h1-a8 diagonal.

 If your opponent acts like the bishop isn't blocked, the discovered attack isn't.

True, but even so, he has to continually keep that in mind, and it further limits his options.

If my opponent is forced to act as though the bishop isn't blocked in order to ward against discovered attacks, then why put my knight in an inferior position just to unblock it?

 Because then they can just decide which discovered attacks are better and you very often just end up with a useless knight if that "discovered attack" doesn't work.

A knight on f3 is far from useless. It's very often the best spot for the knight,  and in most opening positions it's the best square that the knight on g1 can get to without having to move twice. So ideally, I'd like to have my knight on f3. If I also want to fianchetto my bishop on c1 to g2, does that change things? For me, the answer is usually no, as I don't feel the knight being on f3 really diminishes the effectiveness of the bishop on g2.

If you don't value the threat of discovered attacks when the knight moves, and you think that the bishop's influence on the diagonal is hurt by the knight being on f3, and you think the knight isn't valuable on f3 anyway, then you play it the way you think is best. But the reason why so many people do put a knight on f3 when they fianchetto their bishop to g2 is because they're not thinking along those same lines.

I always play Nf3 wtih Bg2 and it makes Ne5 powerful in a lot of lines.  Also, sometimes the knight goes Nh4-f5 (like in the old Indian).  Even if the knight sits there though its controlling central squares.  The f3 square the best square for the knight in general (or so I've been taught).

I'm curious what the strong players will say about this.

It's actually a very good question. In various fianchetto positions a knight on the 3rd (or 6th) rank often WILL need to move again precisely because it's blocking the bishop.

In KIA setups though, for example, the e4 pawn is blocking it already anyway. The point is usually to keep a solid center while seeking play on the flank. If black choose to break with d5, for example, he will give white the option of opening that diagonal.

Having said all that, there are some good attacking schemes with Bg2 and Ne2. It just depends on the opening move orders. If you're playing e4 g3 Bg2 Ne2 as your first 4 moves, black will be able to have more influence in the center than normal. So you can't have everything you want out of the opening... blocking 1 piece isn't something to worry about if your other 3 minors are good, you have a pawn in the center, and your king is safe.

f3 is the natural square for that knight; if you put it on h3, the other dude will take it with his bishop and create doubled isolated pawns on your edge file, and if you put it on e2 it will block up yo stuff and you will spend the rest of the game wondering how to deploy it to maximum effect, and if you don't move it at all, you won't be able to castle kingside.  Robhad's #12 comment is correct.       

Hey guys, no need to hate. He's only a beginner trying to understand why certain moves are played.

There's nothing wrong with e3 and Ne2. That's exactly the idea behind the Rubinstein Reshevsky Nimzo- Indian to avoid the doubled pawns. Though generally there us more potential for the Nf3.

Besides the extra tempo cost for e3, which is often not played early in white Bg2 ideas, check out the immediate mobility from Ne2. Usually the c3 square is taken by the N and g3 is taken. Outposts at d4 or f4 may be useful eventually but are probably just targets into the opening. Not fatal initial lack of mobility and  as you mentioned, it does expand the scope if the Bg2 bishop straight off. So there are tradeoffs.

The mobility from Nf3 appears much greater. As mentioned earlier, Ne5 is a prime location. Ng5 can come in handy in combination with Bg2 and black... Bb7 as in the Monticelli trap. Even in the qid classical, the N vacates f3 to be able to recapture on blacks ...Bxg2 with some ideas. There is also the fianchetto idea of kind of reverse dragon with c4, d3, Nf3 to Nd2 supporting the queen side or center with scope of Bg2.

So either Ne2 or Nf3 are playable. But the benefit is probably going to depend on the plan and immediate opening follow up.