My favorite character to play is a caster. Option 1 (and my first Basic D&D PC, ever, and dozens since across all editions and gaming systems): magely/arcane -without being the "old man/Merlin/Gandalfy"- type. Option 2: followed, closely, by a druid/""nature magic" type, could be staight up "plant magic" or "storm magic" druid, or "storm magey/weather magic" type or "witch" with their "raw/untrained" magic (unlike the refined incantations and gestures of those hoity-toity academy wizards) from the edges of society. Option 3: a tie between casterly-clerics (I don't object to wearing armor or swinging a mace when necessary, but if there's a spell that will be useful, or healing/bolstering my allies, I much prefer that tack) and/or psychic/mental powers type.
Generally males, but have played numerous female characters over the years. Generally prefer an elf or half-elf to a human. Once I really got into D&D, at least. Most of my initial characters were humans. But have, on occasion, gotten the itch for 'something different," in which cases, I've had my share of halflings (my fourth ever Basic D&D PC, and several since) or gnomes (first and best wasn't until late 1e).
Favorites for various reasons: the most recent was from a Pathfinder game: a [celtic flavored] Elf Witch/Psychic gestault character (the party was all gestalt and existed before I joined the game. I was told I needed to make a gestault character) in a homebrew world/campaign, who eventually achieved godhood. He was my first PF character and I just loved it.
My "first ever" character mentioned above, a human mage ["magic=-user"] who was eventually transitioned into a 1e AD&D character and eventually made it to 14h level (some decades ago). A personal best...until this PF elf-witch-god. This character (and several others of these early adventurers) lives on in my campaign world as a powerful NPC, leader of a self-formed organization of guardians of the realms, especially vs. magical threat or any mortals who seek to attain (or destroy) the (catastrophically destructive, but intrinsically necessary) power of "dragon magic." He's the guy I learned the game on. He used magic! Eventually created his own magic items and spells! He'll always have a special place in my "D&D characters" codex. Montor [later added surname] Dragonwing, first son of the Lordmage of Daenfrii and former Dragonmagess (now deceased), the Dragonmage apparent, champion of Wyr, wielder of the Staff of Wyr.
Going back quite a bit of years, and completely different than anything i said above, but a favorite in the sense of "most memorable," fun to play, and rather outside my typical style -both for roleplay and actual playstyle- was a halfling fighter/thief in 2e. A chain & shield wearing, short sword and short bow toting, battle hardened and road-wise halfling's halfling of impeccable valor, unimpeachable integrity, and incorrigible lover [of anything that would have him].
"Garap 'the Bloodhawk'." Three foot five inches of bravado and sincere daring. Inadvisably extroverted and ever [self-assured] "dashing." The proverbial "legend in his living room." He was a hero, in his own mind, constantly looking to increase his "glory/fame," and no one was going to tell him he wasn't the best at what he loved to do. First to charge into battle. First to volunteer to go scout out the dark cavern ahead. First to goad an enemy the party was desperate to avoid. I recall he nearly died in a cavern full of trolls he'd been lowered into. The rest of the party really didn't have means to get to him when he needed assistance....but I don't think he, ultimately, died there...It may be the campaign/game/group just came to an end. Not sure. Don't remember. But a blast to play and very "not my usual" character.
Just so happen to have a [very old] picture of this one, I did, on my computer.