The most popular apps are probably Datavault, 1Password, and eWallet (in no specific order). They have somewhat different feature sets and pricepoints, but all will do the job.
Personally I am using eWallet. This is mostly for historic reasons: it has been available for multiple platforms over the years and I have been using it since back when I had a Palm OS device, so I could simply continue using my existing database. There are desktop counterparts for Windows and MacOS that sync with the mobile version.