Some appliances are intended to be run on their own "dedicated" circuits (air conditioning units, for example), while others, like the microwave, simply eat up so much electricity while running that they tend to very easily trip the circuit breaker, especially if you're living in an older house that hasn't had a wiring update recently. Here are some signs that you do need a wiring update because you simply don't have the circuits that you need to run your everyday appliances safely.
Blown fuses or tripped breakers
First of all, if you have blown fuses, you definitely are heading for an electrical update. Having a fuse box at all means that your wiring system hasn't been updated recently (or at least not sufficiently; modern electricians know that fuse boxes are outdated and that circuit breaker boxes are better). So get that taken care of first. Second, you should keep an eye on how often certain circuits are having problems. If your kitchen circuit overloads frequently, maybe you simply have too great an area loaded onto that one circuit (perhaps the house's electrical wiring was badly designed to begin with). Or if you have circuit breakers tripping frequently but not in any one area, maybe the house's system just needs a total overhaul.
If your lights periodically dim for a brief second when a large appliance switches on, that could be a sign that said appliance needs a dedicated circuit of its own. Of course, dimming lights could be a sign of some other electrical problem, so it's a good idea to have an electrician come in for an inspection anyway. If you haven't had an electrical inspection since you moved in, now is definitely the time.
If you're using power strips or some other method to allow you to plug many, many items into one wall plug at a time, you probably need some electrical work. It's not your fault; many houses simply aren't built with enough wall sockets in the room to support a modern lifestyle. If you don't live in a very new house, this is likely to be the case. So go into your family room and take a look at your entertainment center; do you have more than two or three items all drawing power from the same electrical socket simultaneously? This can be unsafe, so get some electrical work done even if it's just to add more wall sockets near the entertainment center.
These signs will help you estimate whether or not you're likely to have a problematically low number of electrical circuits in your home compared to the amount of electricity that you use. If you recognize yourself in these signs, consider having an electrician in for an inspection, and then listen to his or her recommendations for any electrical work you may need.