Nimzo-Indian Defense [E30-59] 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4
"Black shows a willingness to give up his Bishop in exchange for a free development and play against White's doubled pawns."
The most common reply to Black's pin is 4.e3, The Rubenstein Variation. Second to this is the Classical Variation ( I think this is or was called the Capablanca Variation) with 4.Qc2. White here is willing to waste a little time preventing the doubling of pawns. The Samisch Variation pushes Black to make the decision with 4.a3.
A notable game where White played the Classical line to avoid the doubled pawns, but Black played an amazing game is:
Alexander Kotov - Mikhail Botvinnik, Leningrad, 1939
Nimzo-Indian Defense, Zurich Variation [ECO E33]
1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Qc2 Nc6 5.Nf3 d5 6.e3 O-O 7.a3
Bxc3+ 8.Qxc3 Bd7 9.b3 a5 10.Bd3 a4 11.Nd2 Re8 12.O-O e5
13.dxe5 Nxe5 14.Bb2 axb3 15.Nxb3 Ne4 16.Qc2 Nxc4 17.Bxc4 dxc4
18.Qxc4 Qg5 19.f4 Qg6 20.Rfd1 Nd6 21.Qd3 Bf5 22.Qc3 Be4 23.Rd2
Bc6 24.Qd3 Nf5 25.Be5 f6 26.Bxc7 Rxe3 27.Qc4+ Kh8 28.Bb6 Ree8
29.Qf1 h5 30.Nd4 Nxd4 31.Bxd4 Re4 32.Re1 Rxe1 33.Qxe1 Rxa3
34.Kh1 Ra8 35.Re2 Kh7 36.h3 Re8 37.Qf2 Qxg2+ 38.Qxg2 Rxe2 0-1