Certified True Randomizers is a simple app which provides various ways to make random choices.
It can flip one of 100 coin types; roll up to 6 dice at a time; shuffle a pack of playing cards and pick them one at a time; pick lottery numbers, with support for 170+ lotteries around the world; generate integers according to your own rules, and produce lists of random numbers.
(Please note, while all randomizers are free with the Android app, the iOS build only comes with the coin flipper. The others cost $0.99 each, or you can buy all 5 for $2.99.)
This isn't quite as trivial as you might think, either. This is the official app of Random.org, and the developer claims it "offers certified true randomness, generated with atmospheric noise and independently approved by several testing labs". And so it's more reliably random than the usual computer-generated values. Maybe.
One consequence of this approach is that the app has to be able to go online to retrieve its seed values. If you're offline then you'll need to fall back on flipping a coin (or whatever) yourself.
The app only uses a fixed portrait layout, too, and so won't look great on all devices.
It only works online, but otherwise Certified True Randomizers provides various easy ways to make instant (and truly random, apparently) decisions