http://www.fontshop.com/fonts/downloads/fontfont/ff_din_round_ot/

The black cut would kick teletubby butts…

But seriously, I think DIN Round is one of the most friendly, warm and cheerful looking typefaces out there (especially in the bolder weights), while still keeping trustworthy.
And it’s not overused like, say, Gotham rounded.

Dunno, I'd find DIN much too stiff and mechanical, even when it's rounded...

You might like something in the direction of Sauna, or maybe Bree?

Edit: Wait, I just saw you specified this is for a website. Are you looking for a webfont to use for text, or just something for headings?

Edit 2 (Sorry, I'll stop now): FF Tisa might be great for both.
http://www.fontshop.com/fontlist/families/ff_tisa/

In my opinion really good suggestions so far, especially Din rounded.
I like to add Omnes http://www.dardenstudio.com/galley/?family=Omnes%20Pro