Is 1.... f6 the ugliest reply to 1.e4? Possibly, although maybe 1. ... f5 deserves that title. I'm not even sure 1. e4 f6 has a name, although I know that 1.e4 f5 2.exf5 Kf7! does (The Tumbleweed if you are interested).
However while 1. ... f6 may be ugly, I have at least one game where it claims a high profile victim. Thomas Barnes used it against Paul Morphy back in 1858, and pulled off a victory. In fact the unheralded Barnes seemed to have quite a good record against Morphy (at least compared to everyone else), so may be it was the offbeat that put him off his game.
Morphy,Paul - Barnes,Thomas Wilson [B00]
London m1 London, 1858
1.e4 f6 2.d4 e6 3.Bd3 Ne7 4.Be3 d5 5.Nc3 dxe4 6.Nxe4 Nd5 7.Nh3 Be7 8.Qh5+ g6 9.Qh6 Bf8 10.Qh4 Bg7 11.0-0 0-0 12.c4 Nxe3 13.fxe3 f5 14.Neg5 h6 15.Nf3 e5 16.Qxd8 Rxd8 17.Bc2 exd4 18.exd4 Bxd4+ 19.Nxd4 Rxd4 20.Rfe1 Kf7 21.c5 Be6 22.Rad1 Nc6 23.Rxd4 Nxd4 24.Ba4 g5 25.Rd1 Rd8 26.a3 f4 27.Nf2 Ne2+ 28.Kf1 Rxd1+ 29.Bxd1 Nd4 30.Ke1 Kf6 31.Kd2 Nb3+ 32.Bxb3 Bxb3 33.Ng4+ Kg6 34.g3 h5 35.Nf2 Kf5 36.Kc3 Bd5 37.Kd4 c6 38.b4 Bg2 39.gxf4 Kxf4 40.a4 Bf1 41.Ne4 h4 42.Nd2 Be2 43.Ne4 g4 44.Nf2 Kf3 45.Ne4 Bf1 46.Ke5 Bd3 47.Ng5+ Kg2 48.Kd6 Kxh2 49.Kc7 Kg3 50.Kxb7 h3 0-1