Craigslist, TVGuide, eBay, CleanMaster, Instant Heart Rate. These are all apps I have been using for awhile. Just a disclaimer, these are ones I use on my Android phone. Not sure if all of them are available for Apple.
I love Craigslist, but I wish they would expand and have more areas like the Iron Range. I often browse the Pets and Free sections of this app just to see what is out there in the community. eBay is your standard app. Lets you monitor your auctions, place bids, sell items, search for things, etc. Pretty basic but it gets to the point.
TVGuide is pretty handy. You can just open up the app, find the right day and time, and find out if there is a new episode of the Big Bang Theory on tonight. Much better than dragging out the laptop and searching around for information. It also gives you a synopsis of the episode and tells how long movies are as well as cast members. Also handy for sporting events to see when and who the MN Wild are playing that particular evening.
CleanMaster is good to clean up the cache and other files your system has produced. I try and clean my phone up one a week or so. There is also the option to clean up your memory. So if you are having trouble running apps try the CleanMaster program. But if that doesn't solve it go ahead and reboot your phone.
Instant Heart Rate is one that well, checks your pulse. Just press your finger up to your camera lens and within 10 seconds it will have your heartbeat. You can even store your information and compare to previous times and days. This would be a good app for people who enjoy exercising.