The default Steam UI doesn't handle a bunch of questions that come up for me regularly.
-List friends who already own a game, even if they haven't played it. -List friends who don't own a game. Both of these are visible now on the "X friends own this game" link on the app page.
-Show if you already have a game in your gift inventory Shows at the top of the App page now, right after the name of the game
-Select Friends you are interested in giving gifts, and see immediately if they are lacking a game Go to your Friends list page and click the icon next to the names of people you want to target. If they are missing a game their name will show up in white just under the game name on the App page. If they wishlisted the game the name will be in bright green.
-Find coop games that you share with someone else. This relies on the automated tagging system, since Co-op is one of the features (like "Controller Support" or "Steam Achievements") that gets grabbed when you run the tagging. Then you can go to your friend's list of all games, select the "Filter to games we both own" checkbox and choose to require the "Co-op" tag on the list to the left.
-Find games currently installed that you haven't gotten all the card drops from Added an option for Easy Cards Only at the top of the Badges page, so you can get them before you uninstall the game.
-Filter your gift inventory to only show gifts a particular person lacks
Setup tasks: To start you need to login, go to your Friends page, and click the big blue Scan Everyone button at the top.
Go to your own list of owned games (through your profile -> Games -> All Games Tab). Be sure you are listing all the games, not just the first 10.
If you want to use the automated game tagging (based on genre and some of the other features like Controller Support) you can visit any app store page and click the blue Tag Untagged button in the upper right. This goes through all the games you/your friends own that aren't already tagged in the resource file and scans their pages.
To record your Gift Inventory just go to your inventory page. Shortly after the page loads green text saying "Gift Inventory scanned" will show up