What is the best scrobbler for Last.fm for my iOS device?
Get CloudScrob.

Finally there is an app that ACTUALLY WORKS AND SCROBBLES CORRECTLY.

This app is the best scrobbler there is for iPhone, and I've tried a bunch of them. It scrobbles in batch mode after you've listened to a bunch of songs, and lets you preview and edit the list of songs before it submits them.

And you use the iPod app to play the songs. Unlike iScrob where you had to use that app to play the songs.