My $.05 worth:
#1 You must become more aggressive as you move up in difficulty levels. For warmongers this is obvious but I've always been a builder at heart. Even now that I know better, I am sometimes tempted to have a moral foreign policy (e.g. I won't fight you, Monty, unless you fight me!) and just build temples everywhere. I still sometimes feel a pang of regret when I invade the nice leader next-door (Gandhi, MM, Hatti) for no reason other than brute strategic realism. But on Noble and below you can build everything you want and win without going to war at all -- on Prince and Monarch, you have to take out an early enemy (pre-1000 BC) to have a chance in the later game. It seems like you always start next to horses, ivory, iron or bronze; so beeline to a tech that will give you good early troops using whatever strategic resource is nearby and, before you found your fourth city, chop-rush 5 or 6 of your best units to attack the poor schmuck next-door who only has archers. Don't be moral: kill, kill, kill! Think W. Bush not Warren Harding.
#2 You don't need EVERY building in EVERY city. If the people are happy, you don't need a coliseum. If the people are healthy, you don't need recycling. If the city is deep in the center of your empire, you don't need walls/castles. If the city is surrounded by hills/plains, you don't need a bank or university. Always ask yourself why am I building that? If the answer is nothing better to build, you should be making troops, not another temple! (Pre-emptive building is fine so if your answer is I just planted a bunch of farms and I expect this city to grow rapidly, then you can build pre-emptive temples/aqueduct, etc. as needed) The point is that three temples in each less-than-pop-12 city aren't going to help you when the Praetorians/Cossacks/Samurai come looking for donations, but a few extra axes/maces/bows will! Having extra troops instead of extra temples will also help you be more aggressive (see #1). Needless to say this also applies to wonders -- you don't need to build any wonders at all to win and too many will hurt you because your army will be too small.
#3 Specialize. Have at least one city (preferably surrounded by plains/hills) that just builds troops THE WHOLE GAME. Only stop making troops to build the few buildings needed to keep that city happy/healthy and build more-better-faster-troops (barracks/forge/factory/heroic epic/etc.). Any cities surrounded by grasslands/floodplains/seas/oceans will be your commerce cities. Build villages on the grasslands/floodplains and science/commerce buildings in these cities. These cities will make money and research while your troop city (cities) crank out soldiers. Make one great person city, put lots of farms around it to get the population big enough to have lots of specialists (and great person points) and mines so that you can build wonders in that city to get more great person points. The game is ultimately one of clock management since every Civ has the same number of turns. Your job is to get the most out of those turns as possible. One way to do this is specialization. When you specialize, you save time because you don't have to build every building in every city (see #2). The time you save is the difference between having large standing army ready to attack/defend and being caught with your pants down when your neighbor launches a sneak attack right after you complete your 9th university in a town that only generates 5 commerce!