I can remember way back in Civ3 DG2 or so, some actually wanted roleplay to affect the game (even I wanted that to a minor degree). Now, things like, "Let's not enact the Slavery civic because it's slavery" is letting roleplay get in the way of the game. (One reason we really never pop-rushed or razed our own cities... - Civ3 DG6 was an exception. I seem to recall Falcon02 and Donsig or someone else in a heated debate about that in Civ3 DG1.).
Civ4 kind of takes away the roleplay aspect of building certain wonders in certain cities and other things due to the way the economy/production system works now (i.e., you can't get rich by building roads - roads are less important now, too, and you can't mine every tile now). There is more roleplay in civics, and religion, so a Culture Advisor would actually have something to do now. Cottages/Hamlets/Towns can also add to the roleplay -- suburbs.
Some examples of roleplaying back in Civ3 -
Citizen's Groups. These aren't as popular now, but back in the day (Civ3 DG1), they were wildly popular. There were two large Citizen Groups - "The War Church" (Knight-Dragon/XIII's group), and the "Spice Traders Guild", my group. The groups weren't political (i.e., they couldn't have a voting block, and couldn't force people to vote or not vote), but they could roleplay certain aspects of the game, and even put something in a thread like, "The Spice Traders Guild would like to have an additional source of spices", or "The War Church would love to have the city of Tyre, and will assemble 5 Macemen to help take it.".
City Threads - Usually the mayor, or the person who "founded" the city (it was the name of a city that they wanted) would make this thread, and roleplay activities in the thread. Events in the city would revolve around the actual gameplay. In Civ3 DG1, Thebes and Mephis were the staging grounds of the Iroquois War, Asphinxia Banquet (and The Great Steamed Crab Debate), and storing of artillery to fend off the Iroquois invasion. In DG2, several cities were captured by India, and they were the staging grounds for a resistence movement while our forces recovered and took back the city. In DG7, we had a 5-city challenge, and cities vied to become the best in a certain area. For example, my city had the first of several unit types, and several war-related wonders. Another city was a fishing city (there were 2 competing for that title I think).
Freeform Events - There are events that can be held in a city or province that are usually sports related. We had a boat race in a bay in Civ3 DG1, and a(n American) Football tournament in Civ3 DG2. Civ3 DG2 (which lasted 11 months due to it being on a huge map and on Emperor - nearly 24 hour turnchats!) also had an economy roleplay, plus a "Game of Fuedalism" where players owned certain tiles and gained income. One of the interesting Freeform events was after Civ3 DG1 was finished - the "Advisors Civil War". It started with the "Delphi County" thread when disorganizer didn't agree with how his city was being handled by the DP (designated player - in Civ3, it was always the president, then down the chain of command). So, he revolted. Soon after, different advisored took sides, and it was a "Civil War" - not to be confused with the "Medicine War" (remember that, donsig?).
Roleplay Forum Threads - These were strictly for the roleplay forum. There would be threads such as a pub, or a news stand.
Roleplaying tends to be the most creative during the early part of the game when a lot of users are still around, and during times of war, especially when we're the ones being invaded (didn't happen that often).
