Here is my take. There 3 types of options:
Web based services that fully implement and enforce rules for their games
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Boardgamearena - the best selection in this category by far. These days games are added much faster than normal players will be able to keep up with so there is always plenty to explore. Very large player base, for popular games you will find matches quickly. Good match-making and lots of play modes: real-time, turn-based (with customizable time allowances), Arena, Tournaments. Generally high quality implementations that tend to stay visually true to the physical version of the game. Many games have good tutorials. The premium subscription is not strictly required but an excellent value if you use the site a lot. BGA has been invaluable in my boardgame journey. It has allowed me to learn and try hundreds of games and I must have bought at least 50 physical games based primarily on my BGA experience. Too many favorites to list.
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Yucata.de - moves slower but over the years it has built up a decent repertoire and it has some real gems that you won't find elsewhere. Primarily for turn-based play (unless you find a group of people who commits to quick turns). The UI is a bit quirky but after getting used to it I like a lot of things about it. In my opinion Yucata has the best undo and replay/review implementation out there. My favorites here are Grand Austria Hotel, Newton, Mottainai, Taverns of Tiefenthal, Lorenzo Il Magnifico. Rajas of the Ganges (and Rajas Dice), Targi, Fields of Arle. Yucata has "sold" me a bunch of games too.
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triqqy.com, happymeeple.com, brettspielwelt.de, rally-the-troops.com, boiteajeux.net, warchestonline.com are some other sites that I visit for specific games. These have smaller player bases but worth checking out to see if they have one of your favorites.
Virtual tabletops that don't enforce the rules
- Tabletop Simulator is a desktop app that's available for purchase on Steam. As the name suggests this is a physics based 3d tabletop that allows you to play a huge number of games thanks to a passionate community that implements and provides these via the Steam workshop. You will find just about everything here. The main downside (to some) is that game rules are not implemented or enforced. It's primarily a 3d simulation of the phyisical components. Many games implement some level of assistance using the built-in Lua support, for example they might automate setup or have a button for end-of-round cleanup. But generally it's up to the players to follow and enforce the rules of the game. I don't play a lot on TTS but I use it all the time to get a feel for a game or its components.
- Tabletopia is a web-based alternative to TTS with the same caveats. Smaller selection of games and less flexible UI, smaller (and less involved) community. Some games can be played for free, others require a subscription.
- virtualtabletop.io - is an open-source reimplementation of playingcards.io. You can think of it as a 2d version of TTS. I like this approach a lot, especially for card games or abstract stuff where the physics simulation and fancy graphics wouldn't add much. Relatively small but passionate community.
- Vassal engine - a Java based open-source desktop app. Lots of modules and a passionate community. Worth checking out especially if you are into wargaming.
Apps that fully implement the rules
There are a lot of apps out there, some for mobile, some for desktop (many available on Steam). Most require a purchase. The quality of implementations vary greatly. Some support online multiplayer, some don't or there is no playerbase. Some have nice snappy implementations, others have very poor UIs or go the other extreme and create an overly fancy UI that is too removed from the physical game. This is generally my least favorite option, I will almost always prefer a good BGA or Yucata implementation over an app. There are a few exceptions: Ascension, One Deck Dungeon, Onirim, Sagrada and Paperback are some where I like the app version a lot.