Is there any way to scrobble the songs I listen to on my Android phone to Last.fm?
The easiest way is to install the official Last.FM app, this will scrobble tracks played by the default Android music player, as well as from many 3rd party audio players, like WinAmp.
It doesn't work with some manufacturer customized music player apps (for instance, Samsung have modified the music player app on the Galaxy S's and scrobbling doesn't work from there). I use WinAmp to play my music on my phone, and that happily scrobbles via the Last.FM app.
If you need just scrobbling, I recommend Scrobble Droid. It's only 45k. And works nicely with default music player for me.
I recently switched to the doubleTwister player on my android and was happy to notice that it has an option to scrobble to Last.FM.
I can suggest you to use my new last.fm scrobbler for android: WAIL Beta, you can read about it on the Google Play: https://play.google.com/store/apps/details?id=com.artemzin.android.wail
WAIL Beta will scrobble music you are listening via different players to your last.fm account, also #nowplaying is supported.
At the moment, WAIL Beta supports that list of music players: Android music player, Google Play Music, PowerAMP, Sony Experia music player, Jetaudio, PlayerPro, Shuttle Music Player, XiiaLive, Liquid Bear Beta + some other players, but they was not tested.
I will be happy to hear your feedback! If you got any questions, email me at: artem.zinnatullin [@] gmail.com or here on StackExchange