There's a lot of serieses (sp?) out there. This is a comprehensive guide.
Drizzt's Trilogy (The Foresaken, Brotherhood of the Hand, and Shadow of the Stranger) - Excellent series, only trouble is you can't play with the same party right through. Aside from the difference in combat difficulty, you play different characters in different games - in fact, in Shadow, you meet the character you played in Brotherhood.
Zankozzie's Big Mistake/Chains - These two are a mini-series, though they probably should be stand-alones. No combat, puzzle-based scenarios. If you like them, check out Dirty Gold by the same author - a lesser scenario and not connected by storyline to the others, but in the same style.
Stareye's scenarios - The series begins with At the Gallows, continues with Foreshadows and then Spears (which was made before Foreshadows...), and then Emulations. Stareye's first scenario Spy's Quest is not a part of his series, and I'm not sure if his BoA scenario A Perfect Forest is or not - if so, the connection is slight. Good points, the scenarios are good, and they work well as individual scenarios, so you can enjoy one without having played any others in the series. However, if you do decide to play through the whole series, be warned - they are very big. At the Gallows takes place on an entire continent, and was the largest scenario ever when it came out. Spears is slightly smaller, but still massive. Foreshadows is a movie scenario and thus very quick, but exists mainly as set-up for Spears. Emulations is a good medium-length scenario.
The Arc - While we can argue about the relative quality of individual scenarios, there is no question that this is the best overall series. While there's the occasional let-down in the mix, so many of Alcritas' scenarios are so good, and there's so many of them, that this series is pretty much unbeatable. Unfortuantely, Al has pretty much stopped designing, and the series will almost certainly never be finished. The order they should be played in: On a Ship To Algiers (beginner, small, fairly difficult), Of Good and Evil (large, multi-path, high levels, difficult), Redemption (large, high levels, very difficult), An Apology (beginner, medium length, very difficult), Lamentations (high levels, fairly difficult, not up to Alcritas' usual standard but needs to be played for the overall storyline, fairly small), Falling Stars (large, use the same party from Lamentations, expect to replay it a lot so keep a save file right at the start, mostly not too difficult but has a very mean end sequence), Signs and Portents (movie scenario), and Tomorrow (continue with the same party from Falling Stars and Lamentations, short/medium size, average difficulty). He has a couple of others, but they can be omitted without hurting the story and aren't that great. You can also skip Algiers and Of Good and Evil without many troubles if you like, but you'd be missing out on a couple of class scenarios.
The Echoes Series - Terrors Martyr (going by Solomon Strokes on these boards at the moment) has made a frightening number of scenarios, and a fair few of them are a part of the Echoes series. However, you could probably play them in any order without it making a difference, as the plots are extremely difficult to understand anyway. I'd recommend playing Nebulous Times Hence, which is his best scenario and a stand-alone, to see if you like his style.
TM also made Bandits and Bandits II: Ballad of the Red Star. However, I don't count these as a series. While some of the same characters are featured, Bandits II is much more a continuation of the Echoes series than of the Bandits storyline. Heck, it doesn't even have any bandits in it.
The Spheres Trilogy - From way back in the early days. Riddle of the Spheres was the first decent scenario released for BoE. This trilogy is meant to be played with the same party straight through, using a brand new one for Riddle. Quests of the Spheres is the second in the series and the best by a fair margin, Destiny is the last and while not actually bad, should probably be a lot smaller than it is. The Spheres Trilogy is pretty dated now, so you probably enjoy it more if you played it early on, before moving onto the more difficult and more flashy modern-style scenarios.
The Adventurer's Club Trilogy is comprised of a massive scenario (AC1), a huge scenario (AC2), and the largest scenario ever made (AC3). They are fairly old school style games (AC1 and AC3 in particular), and are good ones to start on if you enjoyed the Exiles and Avernums. Just be warned that it'll take a while for you to finish them.
The lost_king Trilogy - If you value your sanity, never ever play these scenarios.
Demon Island I and II - If you ever choose to play these, use a God party. Mainly it's just kill demons, kill demons, kill demons, but there's some cool technical trickery (especially in Demon Island II) that may make them worth playing. Or may not.
Doom Moon I and II - Start with a medium level party in the first one, and take it into the sequel. These scenarios have really tough enemies, but they also load you up with really powerful weapons. Any party that goes through these scenarios will be too powerful to use again, except for stuff like the Demon Island scenarios. The Doom Moons have a shaky storyline and really bad spelling (English was a second language for the designer), but they also have good puzzles and some really cool technical tricks. Doom Moon II in particular has influenced a lot of designers.
Teh Grich 1 and 2 - TM, designer of the Echoes series, made these. They are very short and are designed as a parody of one of the most hated scenarios ever - The Grinch. Basically, they are intentionally really terrible. May be worth playing, one day.
The Chicken Plague Trilogy - Made by Brave Sir Robin. Haven't played them myself. I gather that essentially you just kill chickens for three scenarios. Was intended as a comedy series, but not appreciated by many.
Our Man Vlad and Our Man Vlad: Redemption - Also by Brave Sir Robin, and also scenarios that I have not played. No one seems to like them much.
The Lost Tunnels Part 1 and 2 - Okay, nothing special, put off these until you're done with the really good ones (which will take a good year or so).
The Kurnis/Uganta series - Four scenarios, designed by myself and my brother under the name of "The Creator". The first, Isle of Boredom, has some bugs and stuff and is the weakest. However, I do think it's worth playing if you like puzzles, combat you have to think about to win, and nifty technical stuff. Ugantan Nightmare was the first movie scenario, and was made in a week to demonstrate this really cool animation trick we'd developed (and has since been used in a lot of other scenarios). To Live in Fear is another movie scenario. They should be played/watched after Isle of Boredom but before Revenge, the last in the series. Revenge is our best scenario, is medium in length, and really difficult. It's also designed so that you don't need to play any of the scenarios before it - however it doesn't work in reverse. Playing Revenge first is fine if you just want to get to the good bit, but will spoil parts of the earlier scenarios. Generally, all of our scenarios are hard and are designed for people who've played a lot of BoE and know what they're doing, so you probably want to hold off on playing them for a while. We also have a couple of small stand-alone efforts called Areni and Deadly Goblins. Our scenarios tend to feature character-driven stories, really nasty combat, and really, really flashy tech stuff.
If I've missed any, I'll add them in later.