Well, it’s sad that no one has been willing to offer their opinions - or at least not the right ones 
- I’ll have to jump in and give you the benefit of my own great wisdom. I’ll only mention the ones I’ve read personally.
Song of Ice and Fire - I think this is an essential series. Love it or hate it, it’s hard to claim to be a fantasy fan if you haven’t read it. It’s probably not the best jumping in point for a lot of reasons, including the fact that it’s not finished, and also because a big part of its fun is that it really plays havoc with your expectations, and those expectations will have been built up by reading other fantasy. But it’s definitely a must-read sooner or later.
A Wheel of Time - this is the other recent fantasy series that I would call essential. Again, you don’t have to love it, but you must have read at least the first few to call yourself a fantasy fan. In fact, you’d arguably get more credibility if you hated it. I’m one of the relatively rare supporters. Even the really bad books in the middle are better than I recalled upon rereading. The series is done, and the last few were written by Brandon Sanderson, and they are really quite excellent. I think it’s worth slogging through the few real clunkers to get to the end.
Earthsea - Meh. Not my thing. Too poetic and vague for my taste.
The Sword of Truth - the first book is a pretty OK ripoff of your standard fantasy series. Poor nobody farmboy type finds out he’s special, goes off on a journey with a wise old mentor, yadda yadda. You know, Star Wars. The books go downhill fast after that. I stopped reading after whichever book it was that was basically 500 pages of telling us how bad communism is.
Belgariad/Mallorean series - I LOVED these books. When I was in junior high. That’s the target audience. Adults will find them less enthralling.
Malazan Book of the Fallen - I’ve read the first three or four of these, and the rest are still on my to-read pile. But for me, they’re a slog. When I’m reading one, I find myself keeping one eye on the page number to keep track of how close I am to being done so I can read something else. That’s never a good sign. A lot of people praise these books for bravely launching right into the action and forcing you to figure out vast swathes of backstory on your own, which is fine if that’s your thing. Me, I figure that there are really good reasons why most authors find a way to give you the relevant backstory - it’s so that you can know what the HELL IS GOING ON. The ones I’ve read have also been Grim with a capital Grim. They’re unrelentingly bleak, focusing on war and death and annihilation and whatnot. Again, that’s fine now and then, but I can only take so much.
Black Company - weirdly, considering what I just said about Malazan, I quite liked this series. A lot of the same criticisms apply - it’s pure military, war, bleakness - but I liked it. I can’t explain why. There’s a bit more lightness in the Black Company, with the occasional people falling in love for a bit here and there. Maybe that helps.
Mistborn - really, truly excellent. I’ve read just about everything Sanderson has written, and while I haven’t yet found one of his I’ve disliked, I do think Mistborn is the best. It’s nice that the trilogy is finished, and the three books make up a complete, satisfying story, but it’s worth noting that it was planned to be the first trilogy of three. The first was set in your standard sword-y medieval setting, the second would be in the same universe, but in a more modern time, and the last would be set in the far future, which I think is a fantastic idea. None of those other books have been written yet. To further complicate things, he HAS written and published one follow-up book set in a railroady Wild Westy time that was apparently supposed to be a one-off just for fun, but which confusingly was clearly ended with a sequel in mind. Well, whatever. Just read the first Mistborn trilogy and enjoy it. Seek out more after that if you like. In fact…
Sanderson in general - he’s working on an epic 10-volume massive fantasy series, of which only book 1 is out. The Way of Kings, it’s called, and I enjoyed that book more than just about anything I’ve read in the last decade or so. Sanderson has been tremendously prolific. While I have really enjoyed everything of his I’ve read, he’s not without flaws. This is turning into another thread. I’ll stop there. But all his stuff is definitely in the “to recommend” list.
Temeraire - this is the “dragons fighting in the Napoleonic wars” series. I’ve read or listened to them all, and they’re OK, but with such a tremendously silly premise that I have a hard time taking them seriously. It doesn’t help that much of the dialogue, especially in the early books, seems to have been written by someone trying desperately to carry on a conversation with Jane Austen. As a biologist, I’m also constantly annoyed by how little thought is given to how the world would have adapted differently to the presence of dozens of breeds of sentient giant predators, but that’s just me.
Gentlemen Bastards - I really really enjoyed these, too. They’re not typical fantasy books. Think more Oceans’ Eleven in a world where magic is going on in the background. Very fun reading.
The Kingkiller Chronicles - Also really really excellent. I’m waiting eagerly for the last book. Highly recommended.
Discworld - also great, but I don’t think of them as a sort of Series that Must Be Read. Back when I had time to read a lot, I’d throw in a Discworld book in between more serious novels. Sort of like a palate cleanser. There’s a lot of complexity in the series (serieseses?), so do some homework before launching in. They’re funny, incidentally - more parody of fantasy than fantasy - if that hasn’t been made clear yet.
His Dark Materials - I read them. I don’t have much memory of them. If you want young adult fantasy, there are better options, starting with Harry Potter.
Dresden Files - I sort of hesitantly like this series. Much like Discworld, they’re silly enough that you feel more like you’re being entertained rather than reading literature, if that makes sense. The first four or five books give the impression that the whole series is going to be very formulaic, but after that he breaks out of the mold and ends up doing some genuinely interesting things with the characters. Some of these choices have been more popular than others.
Guy Gavriel Kay - I really like his stuff, apart from the Fionavir Tapestry, which I couldn’t get through because it felt so much like Tolkein. His other stuff is really excellent. The Sarantine Mosaic duology is my favorite as well. His books are set on a world that is very reminiscent of times and places in Earth’s history, with just a touch of magic to make it fantasy rather than historical fiction. The Sarantine Mosaic is set in a civilization very similar to the Byzantine Empire. Read those, and if you like it, you’ll like most of his other stuff as well.
I’m trying to think of ones that haven’t been mentioned yet. Nothing comes to mind now. I’m sure I’ll come up with more as time goes on.