As @PKumar pointed out in comments, in base R we may use do.call(rbind). Just put it into a function.
stackDataInList <- function(x) {
  return(do.call(rbind, x))
}
stackDataInList(L[1])  
#   ID     value
# 1  a 0.9101742
# 2  b 0.3841854
# 3  c 1.6821761
stackDataInList(L[c(1, 3, 4)])  
#    ID      value
# 1   a  0.9101742
# 2   b  0.3841854
# 3   c  1.6821761
# 4   f  1.4322822
# 5   g -0.6506964
# 6   h -0.2073807
# 7   i -0.3928079
# 8   j -0.3199929
# 9   k -0.2791133
# 10  l  0.4941883
Or use stack and mapply:
stackDataInList2 <- function(x) setNames(cbind.data.frame(stack(mapply(`[`, x, 1))[[1]],
                                                          stack(mapply(`[`, x, 2))[[1]]), 
                                         names(x[[1]]))
stackDataInList2(L[1])  
# ID     value
# 1  a 0.9101742
# 2  b 0.3841854
# 3  c 1.6821761
stackDataInList2(L[c(1, 3, 4)])  
# ID      value
# 1   a  0.9101742
# 2   b  0.3841854
# 3   c  1.6821761
# 4   f  1.4322822
# 5   g -0.6506964
# 6   h -0.2073807
# 7   i -0.3928079
# 8   j -0.3199929
# 9   k -0.2791133
# 10  l  0.4941883
Also Reduce is an option, found here
stackDataInList3 <- function(x) Reduce(rbind, x)
stackDataInList3(L[1])  
#   ID     value
# 1  a 0.9101742
# 2  b 0.3841854
# 3  c 1.6821761
stackDataInList3(L[c(1, 3, 4)]) 
#    ID      value
# 1   a  0.9101742
# 2   b  0.3841854
# 3   c  1.6821761
# 4   f  1.4322822
# 5   g -0.6506964
# 6   h -0.2073807
# 7   i -0.3928079
# 8   j -0.3199929
# 9   k -0.2791133
# 10  l  0.4941883
Data
L <- list(structure(list(ID = c("a", "b", "c"), value = c(0.9101742, 
0.3841854, 1.6821761)), row.names = c(NA, -3L), class = "data.frame"), 
    structure(list(ID = c("d", "e"), value = c(-0.6357365, -0.4616447
    )), row.names = c(NA, -2L), class = "data.frame"), structure(list(
        ID = c("f", "g", "h", "i"), value = c(1.4322822, -0.6506964, 
        -0.2073807, -0.3928079)), row.names = c(NA, -4L), class = "data.frame"), 
    structure(list(ID = c("j", "k", "l"), value = c(-0.3199929, 
    -0.2791133, 0.4941883)), row.names = c(NA, -3L), class = "data.frame"))