A.C.
I've been through this stage several times with my now three year old daughter. I tried following advice about a little "tough" love and just letting her cry, but I found that it made her MORE clingy and the screaming and crying does nothing for mommy's nerves either.
At this age, my Moby Wrap and Calyx (buckle type Mei Tai carrier) were invaluable. They left my hands free to get done what needed to be done while still able to give my daughter the interaction she wanted. As she got a little older, when she was being whiny, it was easy to tell her that if she wanted me to hold her then she had to go in the backpack. Sometimes she wanted to cuddle...sometimes she would get bored quickly and prefer to play rather than ride along.
I am not a believer in exposing children to TV at a young age. I actually got rid of the TV until she was nearly three years old. She had see some at daycare but I really limited it. It isn't a habit you want to form early when their minds are so much better formed by other means.