It really depends on what sort of game you want to play, though.
For Board games; Catan and Ticket to Ride are both good; or if you have big enough tablet / phablet, try the online version of Cards Against Humanity (it's a browser game)
for RPGs; indeed, Square has a lot of games-- the retro ones at least. FF5, FF6, FF4... Although the price is quite much, it's definitely worth the price. For a cheaper, more free(mium) game; I suggest trying Final Fantasy Record Keeper; it's all the battles without the exploring, with a freaking lot of your beloved FF chars.
But other freemium games from Japan seems to have its fanbase too. I dunno about the pay-to-win aspect of it though...
Ingress is good if you like to walk or travel.
ANd I'm sure there's a lot of other games too >_< Pixel Dungeon is a HARD Roguelike game, but if you like a challenge; do try.