I wasn't happy with Civ III, luckily I can say they have corrected their mistakes and Civ IV is once again Civilization!
Major New Game Options
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Civ IV now has new speed options which are a great addition if you need to play quickly, myself though I always choose epic speed as that gives me the civ game experience I know and love. A game then usually takes me a bit over 8 hours.
The game now ships supporting Multiplayer and has received good reviews - I've not tried this feature yet.
Civ 3 vs. 4 Gameplay
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The first thing you'll notice is the graphics are much nicer and some of the advanced keystroke commands are now represented as easy to use buttons.
Units now have a single strength meter helping you gauge your attack success and better yet if you activate a unit and right click on the enemy you will see the odds of success and a summary of that calculation (terrain is important).
There are no longer military leaders and the grouping of troops under them. However your units do receive experience bonuses and you get to elect where that bonus goes: 10% faster healing, +20% attacking cities, etc.
Barbarian encounters still occur as well as Barbarian cities. Now there are also wild animals roaming about at the start of the game. Huts are still here too.
I had thought I read Railroads wouldn't be so important or work like they did before. That is somewhat true, but to a lesser extent then I expected. Railroads come about the same as before and need to be built over roads as before. The difference is now movement isn't unlimited on them though they do allow you to go much further than roads making them just as useful as before but now you do have to consider troop locations on a continent as they can't cross it all in one turn.
Culture is back and as important as ever. Now you can no longer cross a countries border without having a treaty to do so with them or unless willing to declare war on them. This is a huge consideration when building your empire. You can build cities and grow culture to block the opponent from resources. You can build a city in between your opponents to block road access to resources - though you had better be prepared to win the culture war else your city will become your opponents.
Keeping in mind I've avoided the harder difficulties so far (if I put 8 hours into a game I want to be able to win - though that can involve reloading past points before a bad decision) the AI is no longer hell bent on prying you from your technologies or resources. In version 3 I would always get asked for and then attacked for not providing whatever the computer opponent wanted, now it takes many (and I mean a lot) of refusals and still only particular leaders will attack you first. Furthermore the computer opponents don't instantly unify when one country declares war on you - I've yet had to fight a war against allied computer opponents. The computer has shown some brains when attacking (at least from afar) by using multiple boat loads of troops to attack a city making sure the number of attackers outnumbered mine. Unlike with Civ 3 though I've not encountered the computer continuously making hordes of troops - it seems the computer is having to really produce them the same as myself. This allows you to turn the tide if losing a war as the computer will have used the excess troops in attacking and once you get past that initial barrage you can then counter with the buildup you hopefully got producing while being attacked. To put it simply war once again is a viable strategy that works.
There are more ways to win and I find myself experiencing the alternatives whereas before for me it was always a wipe out the computer or space victory. In the past I felt you had to focus on your winning strategy from the get go, now I feel you can adjust the type of victory you shoot for as game goes on. This adds a lot to the game as there is often different viable victory paths to pursue, so don't get down if your initial plan was less than stellar. You may now be better setup for an alternative victory condition. The conditions still include completely wiping out the computer or going to space, but they now also include winning by culture dominance, winning by a combination of culture and population, allied wins, UN win, and possibly more. There's a victory condition advisor button you can check to see where you may want to focus.
City management is now simplified but not like CTP and feels natural as though the game was designed to be done this way from version 1 though it messed up in the earlier releases. You still want workers to improve your land and picking where you begin a city has an impact on its early ability to grow. However now you don't have to worry about having to build improvements just to grow the city and you're no longer limited to just the few squares around the city - culture is major. You no longer have to quell uprisings. What you have to do is provide workers to improve terrain so the city can grow/produce and you may also want to allocate the resources of a city towards a particular scheme: growth, gold, production, etc. which can be done with a single click. I used to find growing a city to be too much of a full time task to bother with considering all the other facets of the game. Now the city takes care of itself and grows and grows with minimal (just the right amount) of attention.
Civ 4 is everything I hoped Civ 3 to be.