Solutions using rowSums() generally outperform apply() ones:
m <- structure(c( 1, NA, 3, 4, 5,
6, NA, 8, NA, 10,
11, NA, 13, NA, NA),
.Dim = c(5L, 3L))
m[rowSums(is.na(m)) != ncol(m), ]
[,1] [,2] [,3]
[1,] 1 6 11
[2,] 3 8 13
[3,] 4 NA NA
[4,] 5 10 NA