I have defined a custom function, like this:
my.fun = function() { for (i in 1:1000) { ... for (j in 1:20) { ... } }
If you replace replicate with rlply from the plyr package, you can use do.call with rbind:
replicate
plyr
do.call
rbind
library(plyr) do.call(rbind, rlply(5, my.fun()))
If you'd rather not rely on the plyr package, you can always do:
do.call(rbind, lapply(1:5, function(i) my.fun()))