I "like" them all, to an extent, but I've always considered the series deeply flawed. Not just in gameplay, but technically; like YayMarsha, I consider the speed a huge issue that no game before FE10 really addressed to my satisfaction. FE10 had 'Off' as an option for animations which greatly speeds gameplay, and I appreciate that. Otherwise...
FE1-3
Have not aged well. Obviously if I'm going to play 1 I'd probably rather just play FE3-1 instead. Or FEDS. I guess 1 is pretty superfluous now.
FE4
The giant maps are pretty to look at and abominable for gameplay. No, wait, they're not even particularly pretty. Apparently every single village in the world is a 2x3 rectangle. Having a horse means being good, otherwise you could be the best character in the game and be nearly useless. Unless, of course, you have a holy weapon. Yeah, they're awesome, but they also completely tank balance because the massive stat boosts mean they either steamroll everyone or you have to make enemies only they can kill. Either way isn't fun.
Weapon balance is nonexistent; axes in particular are just disgustingly bad.
The story tries to be good, but it's impossible to care about relationships when the story jumps past all that mushy stuff like "living with each other" or "developing the characters." Hey, Sigurd fell in love! Now she's knocked up! Now she's gone! Boy, they sure did love each other... um, right? Manfloy is also an idiot villain who is portrayed as some super-teleporting brainwashing badass with a master plan but he doesn't really HAVE a plan after the first gen, actively sabotages Julius's plans for no clear reason but to be a dick to Celice, and can't even notice the one weapon that could completely undo everything he ever worked for is sitting in the castle where he's hanging out.
FE5
Fundamentally the problem with this game is most of the difficulty is strictly artificial. If you don't know what's going to happen, it is grossly unfair to the player. If you do, it is grossly exploitable by the player, possibly to a greater extent than anything else in the series. Giving me the ability to skip entire maps and essentially punishing me if I refuse to take that option is ridiculous game design.
Other things just feel unfinished. The entire magic system, the route split (which barely lasts any time at all), staves and status effects lasting forever, scroll effects stacking to allow uber-growths, low and identical stat caps... it's sloppy. Most characters are rather poorly developed, though that's fairly standard for FE. Capturing is also cool but poorly thought-out, allowing the acquisition of some disgustingly good equipment. Enemies are basically walking treasure chests given their shit stats.
Some skills are just stupid. Nihil is nearly useless because all the badass enemies aren't really relying on skills and scrolls grant crit immunity anyway. Wrath (and the PCC system in general) is godly. Charisma is ridiculously strong in a 1 RN system. Leadership in general is pointless because the only things you can really do to change the matchups are bring Glade and Fin. Two maps more or less split up the leadership stars between bosses to allow you to defeat them and reduce enemy effectiveness, but it barely matters otherwise. How well you complete maps doesn't matter to it or anything that might make it challenging and useful, and the one character you can get with super-leadership loses most of his stars when he joins.
Story is a letdown. It's trying to go into more detail and while I recognize it's limited by FE4's plot framing it, the story within can't seem to decide who the villain is. Is it Blume? Is it Leidrick? Is it Trabant? Is it Beldo? There's lots of scheming but nobody in the villains seems to be plotting against or foiling each other, they just randomly attack you and never each other or otherwise screw each other up. Except Hannibal, whom we already know to be a good guy from FE4. The attempts to further humanize Trabant continue to fall flat thanks to his utter dick move in FE4 ch5. Oh, and then some Dark Warlords show up for some reason at the end, not that you care about any of them anyway as they're just minibosses like in FE4. And then die, but are somehow still there in FE4. Whatever, zombies can do that I guess. Or are they zombies? WHO KNOWS, THEY NEVER TALK ABOUT IT.
FE6
Blandest objectives imaginable. Every map is seize. The endgame is choked with wyverns that ought to be exciting challenges but are pretty much utterly raped by what you will have to bear at the time. Even one map where you had to, say, DEFEND against a wyvern rush would've helped spice things up.
Roy is pointlessly sandbagged for most of the game, and then he barely gets any actual use out of the Sword of Seals and must not use it up lest you screw yourself out of the proper ending. Some characters are godly. HM stat bonus not very well thought-out; I'm pretty sure HM stats aren't supposed to make the game easier (Percival lololol). Speaking of hard mode, it does get points from me for actually starting out really hard, but it doesn't stick. A shame.
FE7
Lyn mode is pretty dull. Supports take an eternity. Otherwise it's okay enough mechanically.
The story is very disjointed and Nergal's entire... well... plan is kind of nonsensical. He gets way too involved in things he really doesn't need to worry about. Honestly, I'm still not sure what the hell half the things he did had to do with his actual plan. Nor why Athos didn't already know what he was up to. He wasn't exactly hiding it and Athos knew MOST of his plan. The whole thing about morphs didn't seem to make a lot of sense either, really. I mean being able to create fake people is a cool power I guess and provides easy minions but how'd he do it? Is it the forbidden magic he's been exploring? It didn't seem especially bad, on balance...
Oh and then you kill Nergal and fight a dragon. A dragon who is actually less culpable for any wrongdoing than Idoun was. He heard some bad shit going down in the other world, went through the gate, and went to help. You're basically kicking his ass for trying to help (and going crazy admittedly, but still). Anticlimax much?
FE8
Obviously, a game the first character you get can solo effortlessly is not well-designed. Oh, and it's short to boot.
I actually liked monsters and whatnot, but there was basically no explanation for 90% of the monsters. Apparently the world is just full of them? They're minions of Fomortiis or something, right? Or... something? What's the point of sealing or killing him if the monsters are just going to keep stomping around doing their thing? Can they be controlled somehow? Lyon can apparently do it, but was that just because of his connection to the demon or something necromancers do?
Eirika and Ephraim were pretty annoying lords. Eirika was probably better off I guess, but she could be quite annoyingly insecure. Ephraim basically never does anything wrong and figures out every plot twist instantly (but not so fast he can avoid falling for most of them, except when he does). They also had crazy-strong personal weapons.
FE9
Class imbalance was quite bad. Paladins were amazing. Everyone else I could take or leave. Many of the larger maps basically were begging to be rushed by a gaggle of awesome Paladins. Skills were pretty tacked-on since they couldn't be removed and most characters didn't really have any (which meant only the ones who started with a skill really had a shot at a skill combo). Enemies weren't very tough, but there were some good difficult early chapters (and then none later). Having to get lucky to make the Black Knight fight winnable (and you might need to level Mist to be sure). Ike was disgusting and Ragnell was just unfair.
The plot makes sense, but Ashnard is a comic book villain with no particularly meaningful motivation to do what he does besides the fact that he's an asshole.
FE10
I like a lot of things about this game. I really actually like the different parts, but the story was nothing special and there weren't nearly enough maps where your two or more groups of characters go up against each other directly (which would've been fun). The Dawn Brigade was hopelessly sandbagged and horse characters were utterly boned after being too good in 9. Haar is godlike in a way that is just obscene, and Ike's early Ragnell is likewise jaw-droppingly imbalanced. Ike gets axes on promotion, but what was the point of that in the first place if he's had Ragnell for several chapters already? Magic wasn't bad, but mages were just weak. Some characters felt tacked on just to provide continuity (Tormod could've either been written out of the story or written back into it in Part 3 so he actually existed). Laguz royals, who ought to be insurance for the final maps, are basically just a WIN button. At least they made skills fun and exciting.
FE11/DS
It's a very lazy remake. On a technical level I suppose it's decently-done, but innovation-wise it's just awful. I realize they weren't trying to take a broad step forward with the series with a remake of 1, but they could've tried a little harder. I mean, what the hell, you add a class swap feature and don't have rescuing? It's hypocritical. "Oh, we're fundamentally changing the very nature of Fire Emblem, but we're not going to add necessary convenience features that have made the series vastly more playable."
Classes imbalanced again, but at least this time anyone can be the broken ones. Too bad some characters are just bad and will essentially never be redeemable because characters who are better can steal their class and do a better job at it. The entire forge system is questionable. The wi-fi store is a bad idea (well, it's a good idea to an extent, but see the next sentence). These imbalances transfer to the multiplayer, which ruins its potential. The extra hard modes are nice, but the game is so boring to play through even once that doing it 6 times or even twice isn't really appealing to me, particularly since nothing really changes besides difficulty.