Photograde (iPhone, Android) and Photograde HD (iPad)
Grey Sheet On-Line
If you subscribe to the Coin Dealer Newsletter, you certainly know its value. You can also get it as a separate subscription as an on-line version. If you attend coin shows infrequently, you'll appreciate that you can get immediate access to the current issue for just $4.99.
Although the app is free, you need a $99 per year subscription to actually get any use from this. Still, this is arguably one of the best general purpose coin apps available, combining pictures, prices and more of U.S. coins by date and variety.
NGC Coin Details
Lets you type in or scan NGC certification numbers and shows you images (sometimes), descriptions (sometimes) and prices/auctions (again, sometimes). Not very useful, in my opinion.
Free, no subscription required. Same information is available on-line at PCGS, but it is much easier to read in the app. The prices do tend to be a little jumpy though when you scroll left or right to select grades.
Again, subscription required. This is access to the ANA's Numismatist Magazine. Pretty nice on an iPad; I haven't used it on my phone.
Although not specifically for coins, this app lets you organize and share collections. It does have coin related layouts, which you can modify to your own likes, so you could have everything you'd want to know about your collection or want lists, including photos, links to other resources, barcodes and more. I haven't yet found the patience or the time to input my collection, but I can see how this could be very useful.
Spot prices and melt calculators. I use it just because it is a quick way to check spot prices.
Note: All my coins are in a safe deposit box. I keep nothing in my home.
Contests and giveaways: http://coins.aplawrence.com/2014/05/contests-and-giveaways.html