Just for completion the data.table solution:
library(data.table)
mydf <- structure(list(ID = c(110L, 111L, 121L, 131L, 141L),
MONTH.YEAR = c("JAN. 2012", "JAN. 2012",
"FEB. 2012", "FEB. 2012",
"MAR. 2012"),
VALUE = c(1000L, 2000L, 3000L, 4000L, 5000L)),
.Names = c("ID", "MONTH.YEAR", "VALUE"),
class = "data.frame", row.names = c(NA, -5L))
setDT(mydf)
mydf[, .(`Number of rows` = .N), by = MONTH.YEAR]
MONTH.YEAR Number of rows
1: JAN. 2012 2
2: FEB. 2012 2
3: MAR. 2012 1