The only time I used a password in a classic Castlevania game was for Super Castlevania IV back during the start of the 32-Bit era of gaming. And the reason for this was because I didn't really like the game enough and just wanted to beat it already without looking back. ... But because I didn't like it much, I also couldn't play it for too long either. So passwords worked wonders for me and this game back then.
But now a days, and since then my first SCIV playthrough back then, I've never used a password or save feature when playing classic Castlevania games. Every time I start a particular classic Castlevania game, I always start from the very beginning and play until I beat the game or until I reach an area that's giving some trouble and I feel I've had enough tries at the moment. Reflect at what a great game it is and how much fun & replay it's providing me. Then turn game off until next time when I again start from the very beginning and see if I can make it past the section that's given me trouble? (Sometimes I'm in the mood to put in many attempts at something giving me a hard time, and sometimes I'm not)
A reason I play like this is because I really love these games (thus don't mind replaying them over and over in their entire), and this is basically how I played most action games back in the day since most of them didn't have passwords or save features (even the ones that did, like the Mega Man games, I never used their passwords when starting another game). And it's not like they needed them since the games themselves aren't that long at all. Same with the classic Castlevania games, which really aren't that long to need passwords (even for part III & IV). But, the convenience is there for those that want it or need it. So my question is, do you use the password feature? And why?