ICO is one of the rarest and most interesting games for the PS2. If you manage to find a copy you'll be able to embark on a great and romantic adventure full of puzzles, magic, and fantasy. As outdated as the game may look right now, it's one of the best-looking early PS2 games. Saving Yorda is in your hands!
Wii Sports (Wii)
Although playing competitive games is not a good idea for Valentine's Day, Wii Sports might be the exception. You and your partner will have quite a lot of fun with this one, whether you choose to play Tennis, Golf, Bowling, Baseball, Boxing, or all of them! You will work up a sweat while playing, and you will laugh for sure!
Rock Band (X360, PS3, Wii, PS2)
How about forming a music band on Valentine's Day? You both can play at the same time, and if one of you is not good at playing the virtual guitar or the drums, just go ahead and sing! After all, how embarrassing could it be when you already know each other? Leave your discomfort aside and have some fun!
Final Fantasy series
Pretty much every Final Fantasy game out there has romantic elements in the plot. If you both enjoy games loaded with fantasy and RPG action, you should play one of them! And if you've played them all… maybe it's time to revisit your favorite one!