Ditto on Slimport! Chromecast and Miracast are too limited. Slimport works with everything, video players, streaming, games...
But 'icwhatudidthere' is right; a few apps don't support 'video-out', so Slimport won't work with those apps. No adapter will, for that matter.
Luckily though, only very few apps don't allow video-out. Mostly its just the stingy Cable TV apps like Time Warner Cable, HBO, and Showtime, etc.
BTW, last I checked, they were almost impossible to get on Amazon. And when they were available, they were somewhere around $35 to $50. They have other, cheaper brands, but judging by the reviews, they're crap.
Your best bet for a Slimport adapter is eBay. I got a genuine Slimport for $16 and it works fantastic. There's a lot of knock-offs out there, so I'd look for a seller with excellent feedback.