The primary purpose of a handyman is to fill the gap between what you or your spouse can accomplish around the house, and jobs that would normally require a licensed contractor. Of course, the gap between those two extremes can be either nearly imperceptible or very wide based on your own skill level and your local building codes. Although choosing to contract a handyman service for your home could be a very sensible decision, this is a decision you should make very carefully.
Handymen are not typically licensed or otherwise regulated, so you can't always presume that a particular handyman has the particular skill set you need. References could settle that issue, but only if you ask the right questions. For instance, one handyman might have done a wonderful job repairing the steps on your neighbor's deck, but that doesn't qualify him to install your garage door opener.
Another complication brought on by the lack of licensing is that sometimes handymen aren't allowed to do certain jobs at all. While most municipalities will allow anyone to install a light switch, they may insist that only a licensed electrician be allowed to re-wire a basement. Plumbing and electrical work are the areas where homeowners often choose to employ a contractor instead of a handyman, but you should also know which construction projects call for some kind of licensing as well. One mark of a reliable handyman is that he will be knowledgeable and very up front about the jobs he can and cannot do.
The primary reason that most people choose a handyman service is to keep their costs down, so price should be a large part of the formula when choosing a handyman. His hourly wage should be reasonably less than the price of an electrician or plumber for the same job. On the other hand, if the price seems ridiculously low, that would be the sign of an inexperienced handyman or possibly a very bad estimate.
If you are able to find a handyman with the right kind of experience, the ability to do the job legally and who is available at a reasonable price, then employing a handyman service could be a very sensible decision. However, in the absence of one or more of these qualifications, you might be better off hiring a licensed contractor to work on your home.