I build Wealth and Culture occasionally; Wealth nearly always (which might be a reason I'm having a hard time).
Culture is great if you're going for a Culture win--obviously. It's also helpful with new conquests, to reclaim their old terrain.
Wealth is good if you're below 100% for Science. You may think Research, but oftentimes the Wealth production will allow you to bump your Science% by a notch or two, which is much more effective than the small amount given by Research. It's also helpful for modernizing your army and/or when you absolutely, positively must have a Wonder (Pentagon, for me). In the latter case, I'll drop my science down to 0% (blasphemy!) and switch all my cities that aren't busy with something else to Wealth, then buy the Wonder with Universal Suffrage. It usually cuts the time down to about 10-15 turns on Marathon, no idea about Normal.