I'll start.
Like many in my generation, I was introduced to D&D through my PC. I played a variety of games as a kid: puzzle games, racing games, strategy games, the works. The first cRPG I played was RuneScape, although that isn't what got me interested in RPGs. I used Runescape as little more than a chat program with built-in theme music and puzzles, it didn't make me 'feel' anything. What really got me into RPGs was Diablo II.
My friend recommended D2, it wasn't new so I got it cheap and installed it. I paid rapt attention to the opening cinematic, as I always did when I played strategy games before it. I chose a character (barbarian), listened to all the NPCs, got my quest, and went out of the encampment.
and It was raining.I hadn't felt anything like that, before. The feeling of immersion, of being in a place you aren't. The simple yet well-done sprite graphics, the ambient sounds, the story, and even the action made me forget that I'm a person playing a game. I didn't get that from any game before that, and when I finished the ending cinematic I felt hollow. I could still play the game for the challenge, like any other game, and I could still play other games, but I couldn't get that feeling back, not nearly as strong.
It was years before I felt that feeling again, and each time it was fleeting. I looked for other games in the same genre and played them all, one after the other, gratuitously pirating and emulating. Some were great at creating that feeling, some weren't. I consumed fantasy fiction by the boatload. I tried finding a D&D game during that time because several of the better cRPGs had D&D's logo on it, but RPG groups are fairly scarce nowadays so it was a while before I really got to play.
When I finally got to sit on a table and play D&D (4th edition), I was disappointed. It wasn't a bad game, but it didn't give that feeling of immersion that I was looking for, the kind the best fantasy games and stories gave. It was essentially just another puzzle game. I spent some time on various online forums and, after about a dozen non-starters, played a few real games online: WFRP, AD&D, RuneQuest. Each died before the campaign was over, but at least it convinced me that tabletop RPGs could give that feeling of immersion after all. I found a FLGS and played a couple of games there too, though they weren't run in the style I've come to understand as creating that feeling. I decided that 3.5 is the closest thing to the game I wanted, and it became my game of choice ever since. There's something about the way characters are built in 3rd edition that makes me imagine them as people, and if the DM and the players run and play the game seriously it can give me that feeling of immersion, of disembodiment, that I am looking for.
I had that feeling before even Diablo, I realise, long ago. D&D, to me, feels like my mother reading stories of old Russian legends, while an early autumn rainstorm beats against the window. The window is slightly open, not enough that the floor gets wet but enough that the sound of the wind and rain gets through.
У лукоморья дуб зелёный;
Златая цепь на дубе том:
И днём и ночью кот учёный
Всё ходит по цепи кругом;
Идёт направо - песнь заводит,
Налево - сказку говорит.
Там чудеса: там леший бродит,
Русалка на ветвях сидит;
Там на неведомых дорожках
Следы невиданных зверей;
Избушка там на курьих ножках
Стоит без окон, без дверей;
Там лес и дол видений полны;
Там о заре прихлынут волны
На брег песчаный и пустой,
И тридцать витязей прекрасных
Чредой из вод выходят ясных,
И с ними дядька их морской;
Там королевич мимоходом
Пленяет грозного царя;
Там в облаках перед народом
Через леса, через моря
Колдун несёт богатыря;
В темнице там царевна тужит,
А бурый волк ей верно служит;
Там ступа с Бабою Ягой
Идёт, бредёт сама собой,
Там царь Кащей над златом чахнет;
Там русский дух... там Русью пахнет!
И там я был, и мёд я пил;
У моря видел дуб зелёный;
Под ним сидел, и кот учёный
Свои мне сказки говорил.
I won't ever be as good of a storyteller as Pushkin, yet I find that the act of building the character and making the character's decisions serve the same purpose: making you think like you're there. That, to me, is what feels like D&D.
I mostly DM now, for a small group of friends. I won't pretend I'm good at it, but DMs are scarce, and DMs that run the way I prefer are scarcer. Most DMs seem to run joke-filled humour campaigns or short strategy combat games, both of which are fine ways to enjoy the game but don't give me that feeling of D&D.