I am not aware of any free apps that are really good, but I have used the Shooter app with reliable results and it goes for about $10 if I remember right. Like any other ballistic computer, it's only as good as the data you put into it, IE knowing your weapon and bullet specs is the key to getting accurate results.
2 best for long range stuff (may not have reticles to pre load) are Hornady 4DOF and Applied Ballistics. Hornady is free- bullet and powder selections are growing but haven’t quite reached what Applied Ballistics has. it’s also used by Mile High Training Detachment and a bunch of Snipers Hide dudes so endusers are testing it and pushing it to its limits.
Applied Ballistics costs a bit and there are some questions about the truing methods they use in transonic and subsonic realms but it has a solid bullet selection and is well used/supported.
Hornady 4DOF is free and will surpass Applied Ballistics as the front runner ballistic solver software and load database. Look for its integration into handheld electronics that are not smart phones soon.
If you're willing to pay $10-12 for an iOS app, MD Ballistics is my favorite for using different reticles, and it's ballistics engine seems to be spot on. It also has the option to use Density Altitude for calculations, which I really like. MD Ballistics also can use multiple b.c. values across different velocity ranges (like Sierra and Hornady publish for their bullets), so that's an interesting step up from most others.
iStrelok has a lot of reticles as well, but I don't like the user interface very much.
iSnipe has the best user interface by far IMO, and has Litz b.c. values in the library, but the reticle options are limited to some basic mil-dot configurations and a few Nightforce reticles. I have used this app more than any others but am starting to use MD Ballistics more too.
I have Ballistic AE (Applied Ballistics) as well, but rarely use it because the user interface is so bad.