RS14: Just some guesses:
If you're going bankrupt, you're probably overspending on services. You don't need Schools/Police/Fire-stations/hospitals until your city has grown a bit. Even when you introduce these, it is entirely reasonable to leave funding very low (<50%) until you can afford to raise their budget. Never skimp on transportation budget, though; that causes your roads to decay.
Remember that you can check your budget at any time. You should try to maintain a budget surplus, generally.
Recessions are harder to diagnose; it would help to know the size of your city. Are they watered/polluted/crime-blighted? My best guesses are the wrong balance of zones (consult the demand indicator on the toolbar) or zones placed too far away for sims to travel between them.
My cities aren't crime central and there always watered and not that polluted.