I was all about the Necro. I basically just maxed out my skeleton
summoning and had an army of minions at my command. Of course his
reviving ability really helped in co-op games, so I usually just sat
back, summoned and watched the chaos unfold with my co-op partners,
raising the dead creatures they killed to further my undead army.
My fondest Diablo 2 memory was when we discovered that the network in my college dorm hall was set up as a LAN environment. The game had just released and my hallmates were all big into it, so we put off our studies in liberal arts and applied our time to darker arts.
I was big into the Amazon. There's something about hailing massive amounts of arrows into swarms of enemies that was appealing. Later sessions allowed me to cheat on my lovely amazon with another, more exotic woman: the Frost Sorceress.
As strange as it sounds, the most frustrating times I had in D2 are the ones that are the most memorable, and ones that I can look back on and laugh fondly. You have to love the curses in the game. Iron Maiden on a melee druid, that one curse that turns you life into your mana on a sorceress... you can kill yourself instantly with the right curse on you. Then comes the scream of frustration, or weary sigh, as you ask the person you're playing with to open a portal so you can retrieve your corpse. Good old teamwork and communication is required to avoid the obnoxious corpse-run ("open a portal! omigosh!"), and who doesn't love that?