Let's say you have data.frames
Plant1987 <- data.frame(plantID=1:4, x=rnorm(4))
Plant1988 <- data.frame(plantID=1:4, x=rnorm(4))
Plant1989 <- data.frame(plantID=1:4, x=rnorm(4))
You could put a $year column in each with
year <- 1987:1989
for(yeari in year) {
  eval(parse(text=paste0("Plant",yeari,"$year<-",yeari)))
}
Plant1987
#   plantID           x year
# 1       1  0.67724230 1987
# 2       2 -1.74773250 1987
# 3       3  0.67982621 1987
# 4       4  0.04731677 1987
# ...etc for other years...
...and either bind them together into one data.frame with
df <- Plant1987
for(yeari in year[-1]) {
  df <- rbind(df, eval(parse(text=paste0("Plant",yeari))))
}
df
#    plantID            x year
# 1        1  0.677242300 1987
# 2        2 -1.747732498 1987
# 3        3  0.679826213 1987
# 4        4  0.047316768 1987
# 5        1  1.043299473 1988
# 6        2  0.003758675 1988
# 7        3  0.601255190 1988
# 8        4  0.904374498 1988
# 9        1  0.082030356 1989
# 10       2 -1.409670456 1989
# 11       3 -0.064881722 1989
# 12       4  1.312507736 1989
...or in a list as 
itsalist <- list()
for(yeari in year) {
  eval(parse(text=paste0("itsalist$Plant",yeari,"<-Plant",yeari)))
}
itsalist
# $Plant1987
#   plantID           x year
# 1       1  0.67724230 1987
# 2       2 -1.74773250 1987
# 3       3  0.67982621 1987
# 4       4  0.04731677 1987
# 
# $Plant1988
#   plantID           x year
# 1       1 1.043299473 1988
# 2       2 0.003758675 1988
# 3       3 0.601255190 1988
# 4       4 0.904374498 1988
# 
# $Plant1989
#   plantID           x year
# 1       1  0.08203036 1989
# 2       2 -1.40967046 1989
# 3       3 -0.06488172 1989
# 4       4  1.31250774 1989