I have played hundreds of hours of these so I'll split them into Board games and Card Games.
Board Games
0. Dungeons and Dragons: I'm putting this at 0 because I'm unsure if it would even count as a 'conventional' board game. I've played a few sessions of this and I had so much fun.
0. Chess: I've played a bunch of national level tournaments of chess (and won a decent few) but, again, I don't know if it would count as a 'board game'
1. Terraforming Mars: Probably the most advanced and highly rated game I've played. Its extremely nuanced.
2. Catan: Probably the board game I've played the most apart from the normal ones.
3. Turing Machine: I got this recently, and have only played it a couple of times, but I've enjoyed the times I've played so I think 3rd is a fair enough spot.
4. Cluedo/Clue (depending on your country): This is a nice strategy based game, basically a less complicated version of Turing Machine (but Clue did come decades earlier)
5. Risk: No one else apart from me likes to play this in my friend group, but I do really like it.
6. Guess Who?: Played it a few times, decent not that good, not that bad.
7. Scrabble: A classic, not that fun, not that bad.
8. Monopoly: First few hours, I'll enjoy a decent bit, but it just gets worse and worse after that, and I can safely say I've never completed a full game of Monopoly. Ever.
9. Ludo: Luck-based. Not Impressive.
Card Games
1. Exploding Kittens: While this may feel a little silly from its name, its an incredibly well made and advanced game, especially when you buy the expansions (I own 2). I've played this the most by far.
2. Unstable Unicorns: Again, ditto. This may feel a bit silly, but its quite strategy-based.
3. Black Queen/Hearts: This is one of the more conventional card games in the sense that it is played using the normal set of cards, but it is really nice.
4. Codenames: Not really a card game, closer to a word game, but fun nevertheless.
5. Happy Little Dinosaurs: From the creators of Unstable Unicorns, it may seem luck-based but has a lot of strategy related to it.
6. ???: We made this game ourselves, its a more complicated, 4-player version of the less complicated, boring 'War', and it adds actual strategy to it.
7. Rummy: A bit too luck-based for me.
8. Go Fish?: Boring, I only play it when nothing else is available.
Some of my favourites: Monopoly
All time classic. One of the best board games ever made. Still play it sometimes on my Playstation.
Hotel
I bought this game with my own pocket money, still have it laying around (at my parents house). Absolutely love this game! It's a bit like Monopoly, but more 'zoomed in' on the properties.
Hero Quest
Also bought this one back in the late 80s/early 90s with my pocket money. Painted all the figures. Created so many scenarios. Also bought some add-ons. Loved this game!
Catan / Settlers
The random board makes it different every time you play. Great game!
Guess Who?
Such a simple game, but so much fun to play. I even created my own characters to replace the default ones.
Board Games
0. Dungeons and Dragons: I'm putting this at 0 because I'm unsure if it would even count as a 'conventional' board game. I've played a few sessions of this and I had so much fun.
0. Chess: I've played a bunch of national level tournaments of chess (and won a decent few) but, again, I don't know if it would count as a 'board game'
1. Terraforming Mars: Probably the most advanced and highly rated game I've played. Its extremely nuanced.
2. Catan: Probably the board game I've played the most apart from the normal ones.
3. Turing Machine: I got this recently, and have only played it a couple of times, but I've enjoyed the times I've played so I think 3rd is a fair enough spot.
4. Cluedo/Clue (depending on your country): This is a nice strategy based game, basically a less complicated version of Turing Machine (but Clue did come decades earlier)
5. Risk: No one else apart from me likes to play this in my friend group, but I do really like it.
6. Guess Who?: Played it a few times, decent not that good, not that bad.
7. Scrabble: A classic, not that fun, not that bad.
8. Monopoly: First few hours, I'll enjoy a decent bit, but it just gets worse and worse after that, and I can safely say I've never completed a full game of Monopoly. Ever.
9. Ludo: Luck-based. Not Impressive.
Card Games
1. Exploding Kittens: While this may feel a little silly from its name, its an incredibly well made and advanced game, especially when you buy the expansions (I own 2). I've played this the most by far.
2. Unstable Unicorns: Again, ditto. This may feel a bit silly, but its quite strategy-based.
3. Black Queen/Hearts: This is one of the more conventional card games in the sense that it is played using the normal set of cards, but it is really nice.
4. Codenames: Not really a card game, closer to a word game, but fun nevertheless.
5. Happy Little Dinosaurs: From the creators of Unstable Unicorns, it may seem luck-based but has a lot of strategy related to it.
6. ???: We made this game ourselves, its a more complicated, 4-player version of the less complicated, boring 'War', and it adds actual strategy to it.
7. Rummy: A bit too luck-based for me.
8. Go Fish?: Boring, I only play it when nothing else is available.
Monopoly
All time classic. One of the best board games ever made. Still play it sometimes on my Playstation.
Hotel
I bought this game with my own pocket money, still have it laying around (at my parents house). Absolutely love this game! It's a bit like Monopoly, but more 'zoomed in' on the properties.
Hero Quest
Also bought this one back in the late 80s/early 90s with my pocket money. Painted all the figures. Created so many scenarios. Also bought some add-ons. Loved this game!
Catan / Settlers
The random board makes it different every time you play. Great game!
Guess Who?
Such a simple game, but so much fun to play. I even created my own characters to replace the default ones.