Depends what you’re looking for and use, really. Are you interested in games at all? I am partial to two, Hoplite, which is a board-gameish game where you move a Greek fighter (probably Jason though they don’t say explicitly) down floors and past demons on a quest for the golden fleece. Very good and the free version is a great game and a full game in it’s own. And they’ll never ask you for money, though more things open up if you give them a little. More free-to-play is Puzzle & Dragons, which does have micro-transactions and an unfortunate ‘Stamina’ system, but is a really good game (think Pokemon mixed with Bejeweled) which you can easily play without ever giving them money. After six months and hundreds of hours and being quite good in the game I only now gave them money because seriously, after that much game they deserve it.
Less gamey, I’ve found apps for my various credit cards are very handy to keep track of everything on the go. Depends on your credit card company, but most have good apps. Similarly, Square Wallet and Softcard (formerly ISIS. They decided they should change the name recently >.<) are handy if you want the ability to pay for things without actually getting out your wallet.
If you listen to Podcasts, I can’t recommend Podcast Addict enough. Very, very good app with lots of options to keep your podcasts sorted and automatically keep them up to date and ready to listen to.
While it’s most likely already on your tablet, Google Calendar is a godsend if you have lots of appointments or, like me, are just terrible at keeping them. Similar for Google Maps.
And miscellaneous, depending on your usage, I use a grocery list app called ‘Out of Milk’ which is decent, handy when I forget what I need and keeps track of prices if you input them, so you can budget easily. I use Feedly, if you use an rss reader for blogs and articles and the like Feedly is a good program for that and having on a mobile device is nice. The Dropbox app is handy if you use it. If you’re like me and use a calculator a lot getting one that’s better than the standard is nice, I use MobiCalc, which occasionally asks for money but it mostly just a really good full-function scientific calculator. Depending on where you live, if you take buses lots of systems now have apps where you can track buses, always nice. If you like music, I also really like subscriptions services, I use Rhapsody, personally, but there are lots and they will let you stream tons of music, ad free, for a monthly fee, and they all have good mobile apps. Screen Filter is random but handy: allows you to tune your screen’s brightness much better than the standard options. Handy for, say, bringing your brightness really low if you’re somewhere dark and don’t want to disturb others, or if you like having the screen on for a nightstand clock, as I do.
So… yeah… I have a few >.>