The ability to sync my google calendar to my phone's calendar is a godsend. I am a ridiculously forgetful person, so as long as I remember to log it in my calendar, there is a nice little pop-up reminding me of what it was I was meant to do!

list of apps I use regularly
Dropbox
Easy Battery Saver (I've noticed a difference when I don't have this installed)
Google Drive
Google Talk/Hangouts
Netflix
Notepad (I use this allll the time)
OneNote
Pandora
Podkicker
SkyDrive
Skype
Snapseed (photo editing)
Whatsapp
Youtube (it's better and faster than the browser version)

And, of course, there are a million social networking, game, and novelty apps. When I first got a smartphone, I went through and downloaded any app that looked like I'd even remotely use it even a little. Over time, I used about 50% of them and they were just taking up space on my hard drive. I would suggest that before you go on a download frenzy, think about if you'll really use something rather than if it's just a cool feature to have available should you ever need to use it.