Paladin: I'm big on knightly virtues, the Gentle Giant archetype that Paladins lean toward, and high-Cha archetypes (because I always prefer to persuade first, with violence only as a lamentable fallback.) I love the idea of Lay on Hands, especially as implemented in 4e, where it is actually self-sacrifice to aid another.
Sorcerer: This was my first love, before Paladin. The idea of magic power coursing through your veins appeals to me, and as above, it's a high-Cha archetype (this will become a running theme.) Even better, the "classic" Sorcerer concept is Draconic, and dragons are one of my favorite things in all of fiction.
Warlord: Leader-of-men, so it's a high-Cha archetype. It's also the class that manifests one of the great distinctions I've always valued, the difference between Athena and Ares: strategy vs. slaughter, brilliant skill vs brute strength, mental combat as opposed to physical combat. Warlords have all that, and diplomacy.
Summoner: Not found in every game, but when it's present, I love it. I'm especially partial to the "Synthesist" concept from Pathfinder, where your buddy acts as a magical-spiritual "shell" surrounding your actual body. High-Cha, dealing with the planes, and full of esoteric knowledge and weirdness--that's my jam.
Avenger: The odd man out, but I've always loved this concept from 4e. It pairs the Divine-flavored stuff I enjoy quite a bit with some unusual elements and an idea of only striking once, but striking with all your might (ultra-accurate and using big weapons, frex.) Plus, Assassin's Creed style, without Assassin's Creed writing.
Now for the "I like them, but not as much as the above" ones. Usually, I'll be drawn in by some kind of other thing, either a cool mechanical interaction or a subclass-/variant-specific descriptive element that excites me.
Druid: Mostly, the thing here is shapeshifting, which has notes of the Synthesist above, but there are others; the 5e circles of Wildfire and Stars appeal quite a bit, and I once, relatively briefly, played a gestalt Int-based Druid/Wizard/Geomancer that was a heck of a lot of fun (and eventually became Space Dragon Pope, only half-joking.)
Monk: I absolutely adore the mechanical implementation of the Monk in 13th Age, and even as a general idea, I find the concept of martial arts pretty cool in a game. Being able to dish out the pain with just your own body, and doing so through patience, discipline, and enlightenment? Yeah, that's cool.
Swordmage: I love finding synergy in seeming contradiction, which runs through several of the above concepts. Swordmages marry together two disciplines usually considered at odds--and I love it when that concept is truly supported to the hilt (hah, punny), making something greater than either part alone.
Warlock: Normally this is outside my wheelhouse, because of the association with corruption and/or "bad" power. But some flavors of Warlock--e.g. Hexblade, or in 5e specifically the Celestial+Tome option--are pretty cool, and I could see them growing into something really interesting and different.
There's also a concept D&D has rarely implemented well, that I wish it would implement better: Runes. I've always wanted a "Runecaster" class that felt distinct and impactful, something that could go toe-to-toe with a regular spellcaster, but in a completely different way, much as how psionics is generally expected to work differently. I take some degree of pride in my command of language, so there's a natural desire to see that control-of-words represented as an actually supernatural power; this is part, albeit only one part, of why I love the Myst games so much.
