[gregorkas]

You should try My Talking Tom - http://talkingtomandfriends.com/tom/. (links to stores in the link). If you're more keen on female cats, there's also My Talking Angela (or other virtual pets from the series). Check it out, it's really well made and tons of fun ;).

[GFischer]

Another very popular one is Pou.

https://play.google.com/store/apps/details?id=me.pou.app&hl=...

It's also an impressive story of a single developer.

http://www.wamda.com/2013/05/the-24-year-old-lebanese-entrep...

I think Pou is much more similar to the original Tamagotchi, and very impressive too.

[krahmal]

https://play.google.com/store/apps/details?id=com.namcobanda... might be a pretty good substitute too.