The ultimate tabletop game database is BoardGameGeek. You can track your own collection, read reviews, leave ratings, and ask and answer questions about rules. You can also log plays of games, as well as wins and losses. Each game's page links to commercial providers, if the game is in print, and a marketplace for second hand purchases.
You can find a number of reviewers who also show playthroughs of various tabletop games. Below are some of our favorites:
Tantrum House: a "group of long-time friends who enjoy sharing [their] love of board games with the world."
Watch It Played: in each video the group teaches viewers the rules, then shows an actual game.
One Stop Co-op Shop: focuses on single- and multi-player co-op games.
Ant Lab Games: not just playthroughs but also the feel of a game so you can decide if it belongs in your collection.