Consider the case where the strings are columns and the result should be a new column:
df <- data.frame(a = letters[1:5], b = LETTERS[1:5], c = 1:5)
df$new_col <- do.call(paste, c(df[c("a", "b")], sep = ", "))
df
# a b c new_col
#1 a A 1 a, A
#2 b B 2 b, B
#3 c C 3 c, C
#4 d D 4 d, D
#5 e E 5 e, E
Optionally, skip the [c("a", "b")]
subsetting if all columns needs to be pasted.
# you can also try str_c from stringr package as mentioned by other users too!
do.call(str_c, c(df[c("a", "b")], sep = ", "))