1. Religion. Religion was just an annoyance in Civ IV for most players and of benefit only to the hardcore. Religion added more onto an already bloated management screen for a player's cities. Conceptually solid, but not much fun in practice.
1. Civ 5 fixes this by simply removing religion in favor of a revamped Social Policies skill tree familiar to anyone that has played an RPG in the last decade.
2. Stacked units. Some Civ fans love stacked units and others hate them. I'm firmly in the hate category. It made it impossible to strategically plan a war as a player's stack or stacks could never sufficiently defend a landmass. Choke-points and bottlenecks were non-existent. Not to mention the headache that it was to manage stacked units.
2. Civ V features one unit per tile gameplay.
3. Too many units. It was amazing how many units that could be built in Civ IV. Micro-management of these forces of war was never-ending, leading to long turn times.
3. Civ V dials the total number of units way down making each unit far more important as they occupy a hex all by themselves. Also some resources are strategic in nature and limit the number of troops of a certain type a Civ can field. For example: a Civ with one iron resource can only have one iron-based unit.
4. I really didn't realize squares bothered me until I played Civ V with it's magnificent hexes. Then I thought about all of the best board games I play: Settlers of Catan, Battle Lore, etc. They all have hex boards!
5. Finally, Civ V puts the smackdown on a lot of other annoyances by simply having a better UI; one that is clear and easy to understand on almost every single screen.