Do tumbling blocks need to be paper pieced?

nope

Not at all...
There are two methods, you can do the traditional block with set in (Y) seams, or strip piece them :D:D:D

Do you know of a pattern for the strip pieced ones?

I hand made one about 10 + years ago, however it was all little pieces. I would like to make another one, so I'm going to keep my eye on this to see if someone comes up with a Tute.

Look on YouTube for tumbling blocks. There is a nice tutorial there for the strip pieced method.

Kaye Wood has an easy method, but of course you need her special ruler to do it with! LOL, I think NOT but then I haven't tried. The paper pieced one on quilters cache is VERY easy to do.

I saw a strip method on a Fons & Porter DVD -it was called Blue Lagoon. The top section was a scrap strip block so Liz did the strips for that block as 2 triangles and then it formed the block "block" when it was sewn. Your library might have it-thats where I got it from.

There is on on Qulterscache.com as well as about.com- it is called "not your grandmother's tumbling block'

I make mine with the WONDERCUT pattern, but you also need their ruler. I love it and it is so simple.