One of, if not the most important app that I have on my phone is LastPass. LastPass is a password manager, now instead of trying to remember dozens of different passwords for various apps and services, I only have to remember one. LastPass is browser based, available on Firefox, Chome, Safari and IE, but also comes with Android, iOS, Windows Phone and Blackberry apps.
LastPass comes with a few great tools, like a password generator, you can have it automatically create complex password, save your log in information and fill out your profile with a few clicks. When you need to change your password for a site, it detects the change and offers to save it for you. LastPass also supports and encourages multifactor authentication to further increase your security. You can add secure notes and additional logins for sites. LastPass also does things like limited credit monitoring, and audits your online security. When the Heartbleed bug was revealed, LastPass proactively started testing sites to let you know if and when to change your passwords.
To use the apps, it takes a premium membership, $12 a year, but I like it because it gives me peace of mind online from identity theft and compromised accounts, $1 a month is easily worth that.