Castlevania 2 has three possible endings. The one you get depends on how fast you finished the game.
First a bit about how time works in the game, for those who don't know. It's displayed in the menu screen in the format days : hours : minutes. Daybreak is at 06:00 hours, and nightfall is at 18:00 hours. As you can see, this makes night and day both last 12 game hours. Time stops when you look at the menu screen, when you're talking to someone, when you're inside a town dwelling, when you're in one of the mansions, and when you're in Castlevania. Uninterrupted, a game hour lasts 15 seconds real-time, making night and day both last exactly three minutes.
Getting back to the endings... to see the first, you need to finish the game in less than 8 game days. For the second, beat the game in between 8 and 15 game days. Take longer than 15 game days and you'll get the third ending. Personally, I think the endings create more questions than they answer, but I'll let you form your own hypotheses about them.
If you just want to get things over with instead of trying to beat the game within 8 days (I admit, it's hard to do unless you know exactly where to go), you can use these NESticle savestates to view the endings of your choice. They are all at the entrance to the final room, where the battle with Dracula awaits. All you have to do is beat him.
Are you playing the game on an actual NES, or would you rather use passwords for some other reason? Alrighty then, here you go.
Ending 1 Password: P0JJ VRBV 22DT TVAZ
Note that if you use a password, you'll always start in the town of Jova, so you still have to get to Castlevania within the time limit for the ending you're going for.