Whenever I start a new character in any Bethesda game(Elder Scrolls and the newer fallout games) its usually a stealthy ranger class. This is probably because those games give extreme bonuses for that play style(instant critical sneak attacks) but I also just like seeing how far away I can be and still kill something. Nothing gives me more satisfaction than being at the draw distance limit and seeing something tiny in the distance fall down. Guns are by far the easiest to do this with but getting the right trajectory on a perfect headshot is way more satisfying when you have to aim at a 45 degree angle to the ground.
 
  The games that I've played so far that exemplify the thrill of archery the most are easily Oblivion and Mount & Blade:Warband. Oblivion handled arrows perfectly in my opinion. The fact that you could actually see and retrieve the arrows from bodies was a great,immersive design choice.Mount & Blade makes archery challenging and rewarding at the same time. In the single player you actually get an experience modifier that is directly linked to the difficulty(range and accuracy) of your successful hits. Multiplayer on the other hand is alot more difficult because the players actively use their shields and evade your arrows, but nothing compares to getting a headshot on a moving horse and watching as your teammates overrun the rider as he gets up from the ground.
 
If anyone else knows of any "realistic" archery in games please tell me in the comments.