I started with Monster hunter Tri for the Wii. I got it pretty much on a whim from seeing it advertised in multiple places and reading an article in Nintendo Power and thought it looked similar to Zelda Twilight Princess. Boy was that a stupid assumption.
I started the game and immediately chose the sword and shield since my favorite series was Zelda and I pretty much wanted to be Link. I did the initial gathering quests and bought some basic armor, and went up through getting the games companion, but I really wanted to see what the online was like. So I hopped online with my terrible internet connection and started questing.
It immediately felt better hunting with other people as I could learn from others, but being on the rookie server meant the other people weren't that much better save for a few. I took down the first 3 boss monsters with a little struggle due to me and others constantly getting disconnected, but I perservered.
After getting to the end of the first batch of quests, I was presented with my first urgent quest, a quest that must be completed to advance to the next group of quests.
At this point, I figured I was fairly good at the game and didn't think it would be that hard, but was still on the fence about how much I actually liked the game. It was this urgent quest where I met Barroth, or as I call him, "the noob killer".
I spent 10 hours on a saturday trying to bring this guy down. Due to getting disconnected and everyone there being so bad at the game, I was only able to attempt it 20 times in that ten hours. I did get advice from some helpful veterans that helped a little (like that I should change my armor since it was the weakest one in the game, lol) but nothing really to get me close to victory. I was getting tired and frustrated, but I was determined not to let this thing win. At this point, I wanted it's blood on my blade and its corpse at my feet.
Eventually, after a 30 min fight, it finally fell. Me and my group were ecstatic and partied in the game for probably ten minutes. It was at this point that the game finally clicked and I got hooked. It's about having the odds stacked against you, and yet still coming out on top. Overcoming obstacles and working together so that when you win, it feels like an accomplishment. Sometimes the rush of adrenaline during the fight, combined with the satisfaction of victory, yields an addiction to the cycle.
I then put over 1200 hours into tri. Then my wii died and I had to start over, but being more skilled, I made much shorter work of getting back to where I left off (I solo'd that urgent quest in ten minutes when I got to it. I wanted vengeance).
That should help explain what makes it so great.