The standard coreutils cp command doesn't support this. There's a Gentoo patch floating around that adds it for different versions, although it's not included in Gentoo anymore for some reason; the version for coreutils 6.10 is in their bugzilla, and I'm sure there are lots of others around.
If you don't want to patch cp, you need to use some other command. For example, rsync has a --progress flag, so you can do:
rsync --progress source destination
If instead of copying you cat the data and then redirect stdout to the destination (i.e. cat source > destination), then you can use a program that measures pipe throughput and insert it in the middle (cat source | SOME-PROGRAM > destination); there are a couple mentioned in this related question. The one I recommended there was pv (Pipe Viewer):

If you give it the --rate flag it will show the transfer rate
cpfor some unknown reason (maybe the trailing?in the question was confusing, but I think that was unintentional). It seems like the opposite of this question – Michael Mrozek♦ Oct 28 '10 at 20:28