I'm a big fan of these series, so there's the possibility of bias, but here it goes:
(Note that these are from the PS2 era; also...WARNING, WALL OF TEXT INCOMING.)
Xenosaga Episodes 1, 2, and 3. It was Monolith Soft's first big series after they split from Squaresoft, and they followed the spirit of Xenogears in making this series. They're also known for making the Xenoblade Chronicles games (which are also spiritual successors to Xenogears and Xenosaga), and have worked on a number of games besides that (including Project X Zone 1&2, and I believe Namco X Capcom).
Xenosaga 1 and 2 were published by Namco, and 3 was published by Bandai Namco. It's a cult hit series, with Episode 1 actually managing to get added to the PS2 Greatest Hits collection. It's a turn-based JRPG series with improved mechanics from Xenogears (save for Episode 2, which took a weird turn due to the team from Episode 1 not being involved. For some reason, they thought switching from mechanics that depended on turn order, 'Break'ing an opponent to prevent them from attacking, and a really engaging card game to a 'zone'-based system where you need to knock down or up an enemy to render then stunned for a turn was a good idea.), elements, special attacks, multi-target attacks, etc. Sadly, I don't think Episode 1 or 3 got a Western release outside of North America; Episode 2 was the only one I've heard getting released in Australia and Europe, and both the title and combat mechanics confused fans when it came out in 2004-05.
On top of that, the Xenosaga series had a host of issues stemming from conflict between Monolith Soft and Namco/Bandai Namco, as well as plans to incorporate a reworked Xenogears into being Episode 5 of Xenosaga. Talks were attempted with Squaresoft, who ultimately refused to let Namco use the rights for Xenogears. Not to mention that the game series was planned to be six episodes, but due to no headway with negotiations and hardware limitations with the PS2, they had to condense what they had going for what was originally Episode 1 and 2 to become Episode 1. Episode 3 became Episode 2, and Episode 4 became 3. Episode 6 was supposed to wrap up the ending to what became Episode 3, but since Xenogears wasn't cleared (and the fallout from Episode 2's changes causing a big fan backlash), the series ended with Episode 3.
It's one of those series that uses data flags to unlock extras in the next entry with game clear data from the previous, like the .hack series. Regardless of all this, it's a pretty enjoyable Sci-fi Opera, and has a number of my favorite characters in the entire industry (I'm a massive KOS-MOS fanboy, and I really like Ziggy and Jin for their backstories and general attitude.). Episode 1 also has long cutscenes. I mean LOOOOOONG cutscenes, surpassing that of MGS4. One sequence of cutscenes was notorious as being over an hour long with no gameplay and three to four save points in between them (though important points in the story and in character development were made during that point in time, and you could save between them, so it wasn't as if you couldn't stop after a certain point and come back.). Episode 3 was also considered the best in the series, due to a good mix of the art styles in Episode 1 and 2, as well as having a slightly upscaled combat system from Episode 1. Sadly, the fallout from Episode 2's drastic change in visual style, it's combat, and the fact that there are no stores to buy restoratives from (making it so that you had to fight to stock up or get said items, increasing the difficulty needlessly) had done a lot of damage, and after Episode 3, Namco Bandai ended the series on a bittersweet note. At least KOS-MOS, T-elos, and Shion have had appearances in Namco X Capcom and PXZ1&2.
That was a lot...now for the other series, which also ended up being a Bandai Namco series. .hack.
First four games were published only under Bandai, and developed by CyberConnect2 (Yes, the same guys who made Asura's Wrath...*sigh*). They were essentially a cyber mystery series based in an online MMORPG (if you've watched Sword Art Online, it's essentially a much better version of that concept, though with less emphasis on action and combat). Gamers falling into comas, main character gets an "item of power" that can have big negative consequences if used unwisely, other gamers who are either affected by these events or are just weird join him, etc. But interestingly, it does give a more realistic depiction of what can happen if "the system" gives you a boost and its administrators don't recognize it, as well as the core of the problem stemming from a man's unrequited love and trying to create an A.I. that was essentially his child.
The combat and some environments were pretty bland, and would've been considered "great" on the Dreamcast, but this series got released from 2003 to 2004 on the PS2 in North America. There was no excuse not to invest some time in better visuals and not simply give alt skins to environments and NPCs. Then again, the series was somewhat popular, since it, .hack//SIGN, .hack//Legend of the Twilight Braclet, and manga series tie-ins did sell pretty well between 2003-2006.
The last three games, the .hack//G.U. series (which were published by Bandai Namco), improved upon the combat and visuals, but it's story wasn't as great as in the initial series. Still decent, but it sort of rehashes the core plot while changing up the flavor. It did have better voice acting (Yuri Lowenthal and Johnny Yong Bosch were two of the main voice actors for the game, and a number of other noted voice actors from anime and video games also worked in it.), and the cutscenes and graphics had a lot more care put into them. Plus, the combat is genuinely fun, if a bit button-mashy. It also had a couple of tie-ins, mainly the .hack/Roots anime (which didn't pull in as many people due to a lack of Toonami during 2007-2009, as well as CN MOVING THE SHOW ALL OVER ITS TIME SLOTS. THAT'S HOW FAMILY GUY GOT CANCELLED AFTER ITS FIRST TWO SEASONS. HAVE NETWORKS LEARNED NOTHING?).
Sadly, the .hack series must've run its course of popularity in the West after that, as .hack//Link was never released (mostly due to the PSP selling poorly outside of Japan), and there have only been a couple of OVAs for the series localized.
Just two series that never achieved their full potential due to issues and reasons outside of their control.
Imma just stick this here.
secure.avaaz.org/en/petit..._for_Global_Release/?pv=3