Today is a particularly useful day for that - as well as one of the Cut the Rope series as the 'official' freebie, there are eight more free ones that usually cost money, including:
Angry Birds - the 'ad free' version, still annoyingly with in-app purchasing.
World of Goo - excellent physics puzzler, building stuff with stretchy blobs of goo. I paid for it via a Humble Bundle.
Paper Camera - I paid for this when it was on sale on Google. It's one of the 'apply an art effect to your pictures' programs, and while it doesn't have many, the ones it has are good.
CalenGoo - a better way of looking at and managing your Google Calendar. I'd still like one like the Psion series 3's calendar, mind.
Swiftkey - the first thing I bought for Shiny three years ago. It's an alternative keyboard with excellent word prediction, saving lots of 'keystrokes'. Since being released, it's been upgraded to have optional Swype-style 'move your finger over the displayed keyboard, and it will work out what word you want from where your finger changes direction'. Highly recommended.
This entry was originally posted at http://lovingboth.dreamwidth.org/499865.html, because despite having a permanent account, I have had enough of LJ's current owners trying to be evil. Please comment there using OpenID - have and if you have an LJ account, you can use it for your OpenID account. Or just join Dreamwidth! It only took a couple of minutes to copy all my entries here to there.