The base R reshape approach for this problem is pretty ugly, particularly since the names aren't in a form that reshape likes. It would be something like the following, where the first setNames line modifies the column names into something that reshape can make use of.
reshape(
setNames(mydf, c("Country", paste0("val.", c(2001, 2002, 2003)))),
direction = "long", idvar = "Country", varying = 2:ncol(mydf),
sep = ".", new.row.names = seq_len(prod(dim(mydf[-1]))))
A better alternative in base R is to use stack, like this:
cbind(mydf[1], stack(mydf[-1]))
# Country values ind
# 1 Nigeria 1 2001
# 2 UK 2 2001
# 3 Nigeria 2 2002
# 4 UK NA 2002
# 5 Nigeria 3 2003
# 6 UK 1 2003
There are also new tools for reshaping data now available, like the "tidyr" package, which gives us gather. Of course, the tidyr:::gather_.data.frame method just calls reshape2::melt, so this part of my answer doesn't necessarily add much except introduce the newer syntax that you might be encountering in the Hadleyverse.
library(tidyr)
gather(mydf, year, value, `2001`:`2003`) ## Note the backticks
# Country year value
# 1 Nigeria 2001 1
# 2 UK 2001 2
# 3 Nigeria 2002 2
# 4 UK 2002 NA
# 5 Nigeria 2003 3
# 6 UK 2003 1
All three options here would need reordering of rows if you want the row order you showed in your question.
A fourth option would be to use merged.stack from my "splitstackshape" package. Like base R's reshape, you'll need to modify the column names to something that includes a "variable" and "time" indicator.
library(splitstackshape)
merged.stack(
setNames(mydf, c("Country", paste0("V.", 2001:2003))),
var.stubs = "V", sep = ".")
# Country .time_1 V
# 1: Nigeria 2001 1
# 2: Nigeria 2002 2
# 3: Nigeria 2003 3
# 4: UK 2001 2
# 5: UK 2002 NA
# 6: UK 2003 1
Sample data
mydf <- structure(list(Country = c("Nigeria", "UK"), `2001` = 1:2, `2002` = c(2L,
NA), `2003` = c(3L, 1L)), .Names = c("Country", "2001", "2002",
"2003"), row.names = 1:2, class = "data.frame")
