In general I prefer original games to "more of the same" sequels. That being said, I suppose "more of the same" is exactly what most people want from sequels, and I might be mistaken, but I would assume that in most cases the gameplay plays a bigger role in why people liked a predecessor than the story and setting. So in that regard, I think it's not such a good idea to switch the genre and still brand the game as a direct numbered sequel. IMO it's fine though to do some kind of spin-off, a game set in the set world but in a different genre.

So, to give some examples, even though they're all still in the same genre, just switching subgenres: Fallout 3 or Doom 3 are already somewhat misleading titles considering what games Fallout 1-2 and Doom 1-2 were, while calling a game with different gameplay Fallout: Tactics or Fallout: New Vegas is totally fine by me. Divinity: Original Sin is a completely different game than Divine Divinity, but then again, it only shares the Divinity to point out the same setting, it's not a direct sequel under the name of Divine Divinity 3 or so, therefor fine by me. I'm undecided about Divinty 2: Ego Draconis, because the 2 is irritating, but then again, it's still different from a title like Divine Divinity 2. Baldur's Gate 3 is a misleading title though, it should have been Baldur's Gate: Original Sin or something like that instead. ;P

Age of Empires went MMO with Age of Empires Online. It was a huge mistake and almost killed the franchise. For a decade there haven't been new installments in the series, only remasters and mods released as DLC for the old games.

There are in my library not a lot of choices to share for this context though you can follow how the genre changed with titles such as civilization and total war. Both games that are immensely popular in a certain crowd and both games have been running for 20 years or longer. Personally i don't like the way these games are currently evolving but lets see, i will be probably tempted enough to buy yet another such title in a couple of years just to see how and what is happening.

Final Fantasy is of course another example of a series that gradually change genre

Personally i don't mind it if it is done right but i do feel a series must know already a firm base, released a couple of titles in the universe before deciding on changing

There is also the odd ones that with their next title try a little change such as changing from real time to turn based ( star drive 1 & star drive 2 ) which by some is already considered heresy

Check out post #3. ;)

Yeah I'm a very casual FF fan and that annoys even me. I never got into Ultima, before my time for the most part, but I'm sure I would be annoyed about that as well.

Perhaps even with Fallout and stuff like that, changing genres should always leave the numbers off and treat it like a spin-off.

It depends on individual preferences. The first Dynasty Warriors was a 1-on-1 fighting game similar to Soul Edge. However, the rest of the series are the hack-and-slash games that most people are familiar with.

As someone that prefers fighting games, which became a niche genre after the 90s, this a loss for me. For Koei, this was a good business decision since they found a formula that kept the series going for nearly 2 decades plus spinoffs.

Touhou did something like that. Touhou 1 is very different from its successors, with having to bounce a ball into cards to complete each level.

After that, all the (integer numbered) games in the series are the bullet hell shmups the series became known for, with only the following exceptions, which are not as big as Touhou 1's exception:
* Touhou 2 apparently had more in common with generic shmups than later games in the series. (IIRC that game may have had a base boss, like the one in the intro stage of The Guardian Legend, and which isn't unusual in the genre (though unusual for Touhou).)
* Touhou 3 and 9 are split-screen, with you playing against an AI-controlled opponent, and enemies you kill may be sent over to the other side. (It may have had offline multiplayer with a human, and I know at least Touhou 9 can be played with 0 human players.)

This happened with the sort of RPGs I happen to enjoy. WRPGs became too action-y and started focusing more on things like NPC interaction, and JRPGs became story heavy, and I prefer my RPGs to be like neither of those.

I don't think it's good or bad per se. I am still open to play Heretic 2, that was a third person action adventure built on the Quake II engine.
The Oddworld series went from sidescrolling to 3d action too, and I don't have a problem with that. I couldn't stand Munch’s Oddysee for the GBA, but it doesn't spoil the series (or rather, the IP) for me. I'll just ignore it.

It's been mentioned, but not concretely. There's Final Fantasy I through X-2, and then there are the two MMOs (11, 14), and then there are the action shitgames (12, 13, 13-2, 13-3, 15, 7-remake, looks like 16.) This is excluding all of the spinoffs and other games using the "Final Fantasy" title that are all over.

Then there was Actraiser to Actraiser 2. One was a platformer and god game. 2 was just the platforming.

Mario was discussed above, and Mario 64/Galaxy/the others in the "3d platformer" side of the series I consider a very different game -- different genre even -- than the original sidescrolling games, and they still make good 2.5d sidescrolling platformers.

However, the sideview vs first person Metroid games could potentially be considered less deviant. It's probably hard to consider them not genre shifting though.

Then there's Zelda (another Nintendo entry) that is COMPLETEL\Y the same game from the shift from 2d to 3d, straight through the original to Skyward Sword (possibly excluding 2). Then they had to do that god-awful Breath of the Wild game that is just bad in pretty much every way and a completely different genre -- and should be put onto a pedestal for how not to design a game [except it has a great intro/tutorial/handhold bit].

In games from companies that produce primarily tabletop games, Mansions of Madness and Mansions of Madness 2nd Edition are quite different. The first one is an asymmetrical game of many vs 1 (though arguably the 1 should have a goal of making a good time for the many, like a GM). 2nd edition is a video game with mandatory tabletop components, many vs scripted AI.

I feel like the "one unit per tile" change in Civilization 5 should be considered a genre change.

Duke Nukem had its arcade-platform first two entries, then the FPS 3d, then a return to arcade-platforming with Manhattan Project. Different genres there.

Genre changes can be good [Zelda, 2d to 3d, but not to open world craftfest]. They can be neutral [Metroid]. But also in many cases, they can be bad. Like Squenix's fuckery with Final Fantasy -- where they continue to convince themselves (despite having data contrary, both from the latest Dragon Quest as well as from Bravely Default!) that turn-based classic-style jRPGs don't sell.

There was a time when they didn't. Specifically, after the release of Super Mario World (1990 in Japan), there were no more "standard" 2d mario games until 2005; that's nearly 15 years? (Albeit a bit less if you're looking at a region other than Japan, but still well over a decade.) (Note that I'm not counting re-releases, Yoshi's Island (which isn't really a Mario game), and Super Mario Land 2 (which was released in 1992 and still didn't quite have the same feel as the classic console Marios).
Reminds me of Dungeons and Dragons, where 4th Edition is very different from all other editions to my understanding (with 5e being more similar to 3.5e than 4e). (4e is still the same genre, however.)

Except for the mandatory insta-fail stealth sections that they insisted in including in almost every Zelda from that point onward.