Ugh this is so hard ;_; I love so many...but if I had to go for Top 5:
1. 999: 9 Hours 9 Persons 9 Doors (DS) - Even when all the mysteries of the game are made clear, I still love playing just because the story and multiple endings are so good. It just draws you in emotionally, and the first time you play you actually feel like your life is at risk and someone has really kidnapped you and placed you on a sinking boat. Even after you get all the endings, it's still fun to play for a lot of them because of how intense they are. I think my favorites would be the True and Submarine endings, because it involves a lot of Junpei x Akane fanservice and just build up on Akane's character (she's one of my favorite characters of all time).
2. Pokemon: HeartGold Version (DS) - Honestly, I would rather have just put the series in general here. It's been a part of my childhood for so long. I met my first best friends through it. And it's just such a fun game to invest all of your imagination into. I get so emotionally-attached to my Pokemon just because after completing the game we've all been through so much. I'm listing HeartGold because I migrated my Ruby team onto it, which is my #1 team of all time (Vileplume, Wigglytuff, Aggron, Shedinja, Altaria, Milotic). My original team on there is also one of my favorites, probably my #2. If I had to pick a game besides this, I'd probably say Red because first gen is the best gen. However Gold was my favorite game and since the internal battery died, HeartGold is the next best thing.
3. Harvest Moon: Sunshine Islands (DS) - Going along with the pattern of games that require emotional investment, Harvest Moon is definitely one of my favorite series. If you don't put your heart into it, it can become very boring very quickly. This game is my favorite of the series because Shea is my favorite bachelor, and even after you get married there's still so much stuff you have to do. I'm approaching Year 6 right now (according to my friend that's a long time for most players) and I can't wait to see our baby grow up.
4. Sonic Adventure DX: Director's Cut (Gamecube) - Probably my favorite Sonic game. What gives this game replay value for me is the Chao Garden. Those things are so adorable and so much fun to care for. <3 Honestly at some points I only go through stages to get animals for them to play with and rings to buy them hats and Heart Fruit. A lot of people prefer Sonic Adventure 2: Battle to this game for the Chao Garden because you can do a lot more with them. What makes up for that in this game is the beautiful scenery. The graphics may not have been as Battle, but I love the atmosphere in all of the stages. One of the reasons that I actually went through stages in this game was because you could enjoy the view along the way. Some of my favorites were Emerald Coast, Windy Valley, Casinopolis, and Twinkle Park.

And the soundtrack was amazing, too.
5. Eternal Sonata (xBox 360) - Definitely my favorite game for this console along with BlazBlue. The places to go are all beautiful and I love literally all of the characters. I wish I had chosen to continue after I finished the story, because the gameplay is really fun and easy to get into. Also making Algretto x Polka canon definitely didn't hurt.

And I love how this game is dedicated to Chopin and the beautiful things he left behind after he passed away, learning about his story while enjoying your own.