I regularly use the technology slider to balance my technology and commerce, but I don't think I've ever toyed with the culture slider. Am I missing out on an important aspect of Civ IV gameplay here? If so, what thoughts/advice can you share on using this slider?
There are several important reasons to consider using the culture slider:
Do you want your cities to grow larger? Culture adds one happiness to each city for each tick used, by itself. If you have any other buildings that use it, Theater (cheap!), Colosseum, Broadcast tower, then you get one more/tick. I generally recommend leaving culture on at least one tick after you get the option, the first bit of happiness is very cheap, and uses your buildings to their fullest.
Cultural Border Expansion
Each tick adds some culture to every city, this means your brand new cities (or pre-owned cities ;) ) start producing culture immediately, and grow to the important 20 squares within a few turns. If you're not playing a Creative leader, this is also a reason I would recommend at least one tick of culture.
If you're headed for this, near the end you'll probably be best off turning culture up as high as you can.
In short, I recommend: Use at least one tick of culture, use the rest to manage happiness.