Hmm... Surprisingly hard to think of games that were great as series. Many good games, very few series that were consistently good or had the great games clearly outweighting the bad ones.
Many "good" series also seem to always have the exact copy of the previous games, which makes it hard to praise as a series rather than praising the single game in the series that did the concept the best. This exludes most Nintendo's series...
1. Metal Gear:
Considering how many games the series has, it's amazing how consistent the quality is. The series has made some drastic choices, but it has rarely if ever let me down. In fact it seemed for long time that each game in the main series just kept getting better than the previous. That is not something most sequels are able to pull off.
2. Final Fantasy:
The king of reinvention while keeping many things familiar. Sure the games might seem and can be accused of being too alike in some aspects, but just looking at how many different opinions and preference you can find among the fans, it's impossible to say they are all the same.
FF fans seem to both love and hate the series and each in their own way. And that's what makes it great. Each game feels both familiar and completely new.
3. Metroid:
Okay, I said something about not putting here self-copycatting series, but I've played only couple of these, which might kinda have an effect on my judgement.
However, the reason I put Metroid here is because it's one of those few classics that managed to make it to 3D not only without losing it's appeal, but turning out better than ever.
How it managed to keep the atmosphere perfectly intact despite being made by entirely different developer and after being turned into a FPS is beyond me.
4. The "Chzo Mythos":
Nope, I don't say this just to kiss Yahtzee's ass. I played these game long before even knowing he had a show on Escapist, and I was stunned how an indie developer had managed to surpass 99% of game industry in the terms of storytelling.
And the games were quite fun to play, unlike most adventure ones. But like said, the plot and the atmosphere is what makes these these games so great, and they feel like you were reading a very engaging horror short story.
The series also knew to stop while it was still good.
5. Kingdom Hearts:
Okay, the main story of KH2 might have been unfinished, short and full of holes in my humble opinion, but I have to ask myself "how bad could the game been, overall? You played it through 5 times for god sake". But either way, while KH2 was a step down...
KH and CoM were awesome. It's sad how underrated CoM is and how prejudiced people are towards it, since its story is pure gold, and you get another one equally good after playing it through.
There's something so absurdly-hilariously epic about how they got all the Disney stuff work for the story. But despite all odds, it works.
And there's just something very bittersweet about the story I find appealing.