There are so many different elements to a single game. There's the gameplay (obviously), the music, ambience, story, characters, locations, and so forth. All of these come together to create one big experience for you to enjoy, all packed in a single game. Sometimes it's good, and sometimes it's bad. But sometimes, it's more than just good: it's amazing. What, in your opinion, makes a good game "good"? Is it any of the aforementioned elements, or something I haven't mentioned at all? On the contrary, which of those elements can just absolutely ruin an otherwise amazing game?
For me, a good game is one that could really draw me into it. I don't care much about graphics. I just need a story that will make me interested enough to continue playing. I've played many top quality games but I haven't finished many of them. No matter how good everything about the game is, if I lose interest in the story, I usually just stop playing. I think I've set a pretty high standard for good games over the years.
A good game is a game that makes you want to actively play it. This may be because of likable characters and an alluring plot, or an amazing gameplay that you can't just help but want to play. Ultimately, I don't believe a good game needs to be perfect in both of these aspects, that'll just make a game a true masterpiece. Platinum games are usually great games with amazing gameplay and a lackluster story for some, while Yoko Taro was known for having underwhelming gameplay (Drakengard), but a fantastic story. That's my take on what makes a game good.
A good game for me has a good story. I am really story oriented and just mechanics or graphics aren't enough to keep me actively wanting to play it. I hate bad plot devices and faulty mechanics though. Can't stand that.
Ideally, the best would be a combination of a lot of features, but what would capture me personally in a game is the storyline. Next to that would be the gameplay (whether I can actually play it or not, is it exciting or more relaxing etc.), and next would be a nice cast of characters with personality.
For me a good game has a majority of the following Great Soundtrack Engaging Story line Fun Multiplayer / Online Play A variety of playable characters / customizations Minimal lag A significant number of achievements and unlockables Easter eggs and in game secrets