You didn't like Lyn, nor Elliwood nor Hector in Blazing Swords?

You should see the japanese one too, so you are sure the problem isn't the english voice acting.

https://www.youtube.com/watch?v=ik4JI4D7rZQ

I played through it in Japanese first. The laugh scene is always bad. But I did like Tidus a lot more in the Japanese version. Yuna as well actually. I was surprised at how her English voice actor suddenly made me lose empathy for the character. Haven't encountered this in any other game I've played both in Jp and Eng since.

As for me, I'll echo "the first half of Tales of the Abyss". But that was obviously intentional by design. They really accomplished their mission though.
I'll add Vaan from FFXII as well. He didn't feel like he added much to the story, or that he was much of a protagonist.

Well, as my Japanese improved, I became less motivated to replay games again in English. Not only due to the language, but also because I find it less motivating to replay games in general today, rather than moving on to one of the many games I still have left to play.

If we're talking about playing through games (with voice acting) that have an actual story and fleshed out character development (not fighting games, or Dynasty Warrior's-esque type of games) from start to finishin in both languages (not switching audio mid game), then the number might be around 7 games.
Suikoden IV, Suikoden V, FFX, Kingdom Hearts, Xenosaga, Tales of the Abyss, Persona 3. I might have forgotten something.

I'm playing Lightning Returns right now, and switched audio midway through. But that's not quite the same thing, as I don't know how I would feel about the earlier events in a different language until I experience it. FFX taught me that.

For FFX it was the only time I felt that I was playing a completely different game the second time around in terms of atmosphere and story. Several voice actors felt innapropriate. Yuna sounded sedated, lacking passion/conviction in her delivery. Similar to Aeris in the english version of Kingdom hearts II, though not nearly as bad. Seymour got a latino voice actor that sounded like he had something stuck in his throat, and didn't sound villainous at all. This was in huge contrast to the very soft/calm and cool villanous voice he had in the Japanese version. And then there's Tidus. Since he had Ichigo's VA in Japanese, he was always the squeeky type, but the delivery of James Arnold Taylor was attrocious. And the voice was much less plesant to my ears.
Among the few characters they managed to re-cast correctly were Rikku and Auron. Following Itachi's Japanese VA might not be an easy task usually. But in Auron's case all they really needed was a deep voice speaking calmly, since Auron isn't very expressive or emotional in the game. However, in the English versions, most characters pronounced his name "Oren", which bugged me, since that's clearly not what アーロン (Aaron) is refering to.
There were a lot of other localization changes as well. High Summoners were now called Meisters. All the final weapons mysteriously changed names for no apparent reason. (Tidus' Ultima Weapon for example was changed to Caladbolg. Now that's a name that rolls of the tongue easily. Caladbolg...) The font of the numbers that appear when you damage enemies also changed into a thicker and quite different font. Etc etc. I can go on and on about all the changes. But in combination with the (for the most part) poorly casted main characters, it all resulted in me feeling no empathy for characters I previously liked. And made it feel like I was playing a completely different game in terms of atmosphere and story. And that was a very strange experience for me. Because while I've certainly felt differently about characters or the story when experiencing them in two different languages in games or anime, it was never this extensive.

Which games have you felt like this about, and why?

Ah, ok. Well, losing empathy for a character, and feeling like you're playing a different game are different things. Although the former can affect the latter.
I thought you were asking me for games where both occured. I can mention many more where I didn't like the characters because of their VA. Let's take Yuri and Karen (who are originally from Shadow Hearts) in the cross over game Chaos Wars. https://www.youtube.com/watch?v=BAtC1SzWSXg
And pretty much every other character. A game with arguably the worst voice acting ever. The producers hired their friends and family to do the English voice overs.

But yeah, I didn't like Millia's English VA either. Didn't feel like it fit the character. I also didn't like Fuuka's English VA, although I felt like it could fit her. Still didn't like it though.
Did you play through those two games in different languages? Because I wonder if already experiencing a character's story and liking that character might make it more difficult to dislike them when you later hear them with a bad voice? Because you already know the character's story, so at times you can think and feel about certain things rather than listen, if that makes sense. I would think it can do that to some extent at least. Perhaps that's why I was all the more surprised in FFX that I suddenly didn't care for Yuna at all.

But this all makes you think about what a "bad protagonist" really means. It could be that some times under different circumstances, you'd consider that character good.