My advice is to trust no one but those weaker than you. The others, if nearby, need to have a close eye kept on. Always ensure you have a sizeable defense along the borders in fortresses and the fronteir cities. As you establish a solid defensive front, go for culture with your cities in the rear, keeping an eye on the surrounding coast (if any) for wandering foreign ships.
If your neighbours are more interested in their military and your conquest, then they'll neglect culture and leave themselves open for cultural assimilation. So long as you have a strong defense (comprised of the strongest defensive units and some offensive (artillery never hurts)) than you should be able to sit tight, quickly develop your culture and technology, get fat and rich off good trade negotiations (if you have extra luxuries and resources) and prepare for whatever victory it is you have in sight. But try to make sure of one thing: Never let other Civs get a lot more land than you. If expansion means conquest, you may have to go for it, unless you feel comfortable enough with a far smaller, compact Civ. I know I rarely do. Civs with a lot of decent land than you (not so much that a lot of their cities are corrupt) can develop technologies, units, luxuries and resources (therefore money) far more rapidly. This means larger armies, more influential cultures, a bigger economy, higher tech and the opportunity to wipe you off the map.
So if you're near the Russians, Persians, Zulus, Aztecs, Egyptians, French, English or Germans, keep your eyes peeled, or get your a$s pealed.
-Maj