Should you bother? Emphatically, Yes, absolutely. If you need more clarification or suggestions on where to start, read on (yes, this is one of my long posts).
Short Version:
Symphony of the Night
Rondo of Blood
Super Castlevania IV
Castlevania
Castlevania III
Bloodlines
Optional: Castlevania Adventure: Rebirth, Aria of Sorrow, Order of Ecclesia
Really Optional: Castlevania II: Simon's Quest
Despite falling off in recent years, Castlevania remains a significant series for anyone interested in retro gaming, the origins of the platformer genre, and (most importantly, in my eyes) game design. Where the early NES is filled with lots of fast, twitch-based platformers, Castlevania is visibly slower and less agile when it comes to gameplay, in a good way. The pace is different, more cautious and you don't feel like you're playing an insanely springy cartoon mascot. You're playing a human being with a whip in a castle full of evil.
Whew. Game-designy rant out of the way, here's my suggestions;
Like the rest of the thread, I will suggest starting off with Symphony of the Night (available on XBL, PSN and PSP) simply for sheer availability and because it's no where near as (blissfully) difficult as other games in the series. You might die a couple times in SotN if you're not paying attention, whereas the earlier games will curbstomp you when you're at your best (don't let that scare you, the difficulty level is part of the series' charm and popularity).
While playing, bear in mind that the rest of the games are pretty much linear platformers rather than the open Metroid-esque exploration of SotN (which was supposed to be a one-shot 'side story' rather than a new direction for the series).
After Symphony, I would suggest either Rondo of Blood (Wii's Virtual Console or PSP is your best bet) or Super Castlevania IV.
Rondo is actually the first part of Symphony's storyline and features many of the same characters. The art style is also similar and the gameplay is all of Castlevania pretty much perfected. It has multiple routes, but is pretty much a linear adventure like the early games.
Super Castlevania IV, on the other hand, is pretty much the first 3 games of the series brought up to a new level, with some little extras like multi-directional whipping. It's not as pretty or as fluid as Rondo, but it represents the early games very very well (including their music).
After that, you're heading back to the absolute roots of the series; the original Castlevania, and Castlevania III: Dracula's Curse (both from the NES). I would also suggest Castlevania: Bloodlines (which was originally on the Sega Genesis). All three should be on the Wii Virtual Console and... ahem... certain sometimes-frowned-upon methods of playing old console games on your PC that might be a violation of NeoGAF TOS and will therefore remain unnamed.
The original game is controller-breakingly difficult (I can claim at least two direct controller replacements to the game as a kid), but again, don't let that scare you. It's part of the series and when you finally do beat it (assuming you beat it), you'll feel like a gaming God. Seriously, beating Castlevania is all the credentials you'll need to be certified as a Badass Gamer of the Old School. The reward is knowing you're among a very small group of people with the ability to become one with the controller and get that Belmont Bastard through insanity.
Do not feel bad using save states. If your objective is to experience the series, use save states rather than burn yourself up. Even on my subsequent play-thrus, I use save states just to save money on Aleve.
Castlevania III is not quite as tough, but still fairly difficult (all of the early games are). It introduces multiple playable characters and alternative routes through the game, but nothing groundbreaking in this day and age (back in the 90s though?). The level design is a little sloppier than Castlevania, but the music is great and there are lots of "Castlevania Moments" that merit a playthru. On that note, Castlevania is well known for its fantastic soundtracks and atmosphere, so make a point to try and enjoy both as you go along.
Bloodlines was sort of a side-story that tried to tie Castlevania to the Bram Stokers novel, and it ends up a mess. Plus it's set during World War I, which is just all sorts of strange (there are 'nazi skeletons'). But the gameplay is fantastic, the level design is nice, and the game is bold enough to go in some interesting directions that the other games never do (for example, the entire game after the first level takes place outside of Castlevania). There's some cool effects in the game too that are worth seeing.
As far as other games of respectable quality, you might try Castlevania Adventure: Rebirth (WiiWare, a remake of one of the Gameboy games that is fairly recent and supposedly decent), Aria of Sorrow (GBA, another Metroidvania), and Order of Ecclesia (sort of a hybrid Linear/Metroidvania thing going on).
There are a few other games in the series, most notably Castlevania II: Simon's Quest that are somewhat optional. CVII was very much ahead of its time, with a large, non-linear world to explore, items to collect, RPG-like systems, and some gameplay elements that would now be categorized as "survival horror". It suffers from a very bad translation, a very strange quest, and some poor design choices. I never beat it as a kid, but did so a few years ago. I needed a walkthru and save states to keep my sanity, it's that rough. Give it a try if you're curious, but it's definitely the black sheep of the series despite having a lot of great "Castlevania" moments and audio tracks.
There are a lot of handheld Castlevanias that are more or less formulaic clones of Symphony of the Night. You can safely skip all of these as I have already mentioned the best of them (Aria and Order).
We do not speak of 3D-Vanias here. Okay, we might as well, actually. Lords of Shadow is alright, I guess, though it's obvious the Castlevania elements are largely painted onto a game that had nothing to do with the original series. Lament of Innocence is respectable for the time, but still not very good. There was one other, but it is trash.
There was also a Castlevania fighting game. You can get the experience of playing this game by taking something you love, raping it, murdering it, and then flinging around its entrails while screaming "Weeee!" until you are arrested.
I tend to replay SotN on a yearly basis (usually around Halloween) and poke at the original, CVIII and Bloodlines every year or so too, just for nostalgic value. Great series, definitely worth a try. If you read this long, please give yourself an internet cookie, you deserve it.