Depending on what you're looking for, one of the following should help you on your way:
Some sample data to start with:
mydf <- data.frame(A = c(1, 2, NA, 4), B = c(1, NA, 3, 4), 
                   C = c(1, NA, 3, 4), D = c(NA, 2, 3, 4), 
                   E = c(NA, 2, 3, 4))
mydf
#    A  B  C  D  E
# 1  1  1  1 NA NA
# 2  2 NA NA  2  2
# 3 NA  3  3  3  3
# 4  4  4  4  4  4
If you wanted to remove rows just according to a few specific columns, you can use complete.cases or the solution suggested by @SimonO101 in the comments. Here, I'm removing rows which have an NA in the first column.
mydf[complete.cases(mydf$A), ]
#   A  B  C  D  E
# 1 1  1  1 NA NA
# 2 2 NA NA  2  2
# 4 4  4  4  4  4
mydf[!is.na(mydf[, 1]), ]
#   A  B  C  D  E
# 1 1  1  1 NA NA
# 2 2 NA NA  2  2
# 4 4  4  4  4  4
If, instead, you wanted to set a threshold--as in "keep only the rows that have fewer than 2 NA values" (but you don't care which columns the NA values are in--you can try something like this:
mydf[rowSums(is.na(mydf)) < 2, ]
#    A B C D E
# 3 NA 3 3 3 3
# 4  4 4 4 4 4
On the other extreme, if you want to delete all rows that have any NA values, just use complete.cases:
mydf[complete.cases(mydf), ]
#   A B C D E
# 4 4 4 4 4 4