I've used the Open Caching app on Android a little, and it seems to work well. Open Caching is different from the "Geocaching" app from Groundspeak (the main geocaching app that everyone uses) in that it is free and open, not only to search for caches, but to place them, etc and requires no membership and has no fees. Here is a quote from OpenCaching.com:
We believe that geocaching should be as free and open as the great
outdoors, so we built a place where anyone with a compatible
GPS-enabled device can upload, download and log caches. No
subscriptions, membership fees or paid content.
That doesn’t mean
we’ve sacrificed any features, though. With support for a broad range
of GPS-enabled devices, including those with eco-friendly “paperless
geocaching” capabilities – it’s the perfect tool for everyone from
beginners to advanced trekkers.
Of course, a downside to freedom is the fact that fewer people use Open Caching which means that there are less caches. I personally consider it worth the price however.