Hearthstone mods is a weird world. With no direct access to the code, but a relatively simple interface that runs on anything and most commonly windowed, it's all done through overlays and APIs. Outside programs that run 'on top' of the client to display information - like auto-updating decklists that show which cards remain in a deck mid-game. Most higher-level players use them, though obviously not in tournaments, and Blizzard says they can't approve, but aren't going to ban you for them either, just that it's on you if the program is updated and something goes wrong. Innkeeper comes to my attention via fansite Hearthpwn, one of the Curse series in association with the likes of MMO-Champion and Diablo Fans, and has some seriously useful bits.
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Its main function is deck-tracking, automatically displaying all your custom-built decks, anything you've done in the Arena and any Tavern Brawl stuff as you play. It has themes to customise the look and lets you turn off the auto-updating nature if you just want a cardlist and to keep track yourself. That stuff is cool, but standard, and it's how Innkeeper integrates with Hearthpwn's huge and widely used online deck builder and database that makes it really interesting.
Innkeeper also tracks your entire collection and uploads that data to Hearthpwn. The site can then tell you things like how much dust you need to complete a full collection of a set, or how many cards of a certain type you have. It's searchable and viewable without booting up the game. This takes the upcoming changes to how formats work into account, meaning you can limit it to just telling you about Standard cards.
But the real impressive stuff is how this meshes with the deck database. Innkeeper will tell Hearthpwn what you have and then the website can tell you how much dust you need to craft a certain deck. Either it will say you're good to go because of your collection, that you need to spend some dust, or that you don't have enough. This has various search functions, letting you say "only show me decks I can craft now" or ones that cost less than a certain amount of dust. Since the Hearthpwn database is updated so regularly - with decks from amateurs and pros alike, either by those people themselves or fans - that's immensely powerful for saving time.
You can read more about it in Hearthpwn's post, as well as grab a download. In combination with Blizzard's own recently announced Hearthstone deck recipes, deckbuilding's getting a lot easier. Hopefully the new set, due to be announced on Friday, makes these tools even more valuable.