df1 <- data.frame(c1=c("a","b","c","d"),c2=c(1,2,3,4) )
df2 <- data.frame(c1=c("c","d","e","f"),c2=c(3,4,5,6) )
> df1
  c1 c2
1  a  1
2  b  2
3  c  3
4  d  4
> df2
  c1 c2
1  c  3
2  d  4
3  e  5
4  f  6

c1 c2
1  a  1
2  b  2

df1[!duplicated(rbind(df2, df1))[-seq_len(nrow(df2))], ]
#   c1 c2
# 1  a  1
# 2  b  2

dt1 <- data.table(df1, key="c1")
dt2 <- data.table(df2)
dt1[!dt2]

setDT(df1)[!df2, on="c1"]

require(sqldf)
sqldf("select * from df1 except select * from df2")

##   c1 c2
## 1  a  1
## 2  b  2

df1 <- data.frame(c1=c("a","b","c","d"),c2=c(1,2,3,4), indf1 = rep("Y",4) )
df2 <- data.frame(c1=c("c","d","e","f"),c2=c(3,4,5,6),indf2 = rep("Y",4) )
merge(df1,df2)
#  c1 c2 indf1 indf2
#1  c  3     Y     Y
#2  d  4     Y     Y

bigdf <- merge(df1,df2,all=TRUE)
#  c1 c2 indf1 indf2
#1  a  1     Y  <NA>
#2  b  2     Y  <NA>
#3  c  3     Y     Y
#4  d  4     Y     Y
#5  e  5  <NA>     Y
#6  f  6  <NA>     Y

bigdf[is.na(bigdf$indf1) ,]
#  c1 c2 indf1 indf2
#5  e  5  <NA>     Y
#6  f  6  <NA>     Y

 bigdf[is.na(bigdf$indf2) ,]  #<- output you requested those not in df2
#  c1 c2 indf1 indf2
#1  a  1     Y  <NA>
#2  b  2     Y  <NA>

df1[!(df1$c1 %in% df2$c1), ]

na.omit( df1[ sapply( 1:ncol(df1) , function(x) ! df1[,x] %in% df2[,x] ) , ] )
#  c1 c2
#1  a  1
#2  b  2

setdiff.data.frame <- function(x, y,
    by = intersect(names(x), names(y)),
    by.x = by, by.y = by) {
  stopifnot(
    is.data.frame(x),
    is.data.frame(y),
    length(by.x) == length(by.y))

  !do.call(paste, c(x[by.x], sep = "30")) %in% do.call(paste, c(y[by.y], sep = "30"))
}

# Example usage
# remove all 4 or 6 cylinder 4 gear cars or 8 cylinder 3 gear rows
to_remove <- data.frame(cyl = c(4, 6, 8), gear = c(4, 4, 3))
mtcars[setdiff.data.frame(mtcars, to_remove), ]
#>                 mpg cyl  disp  hp drat    wt  qsec vs am gear carb
#> Hornet 4 Drive 21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
#> Valiant        18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
#> Toyota Corona  21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
#> Porsche 914-2  26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
#> Lotus Europa   30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
#> Ford Pantera L 15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
#> Ferrari Dino   19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
#> Maserati Bora  15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8

# with differing column names
to_remove2 <- data.frame(a = c(4, 6, 8), b = c(4, 4, 3))
mtcars[setdiff.data.frame(mtcars, to_remove2, by.x = c("cyl", "gear"), by.y = c("a", "b")), ]
#>                 mpg cyl  disp  hp drat    wt  qsec vs am gear carb
#> Hornet 4 Drive 21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
#> Valiant        18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
#> Toyota Corona  21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
#> Porsche 914-2  26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
#> Lotus Europa   30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
#> Ford Pantera L 15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
#> Ferrari Dino   19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
#> Maserati Bora  15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8