The word pergola is taken from the Latin word pergula, which translates as projecting eave. Eaves are, of course, the overhanging edges of a rooftop, and some pergolas are attached to the side of a home, with the roof of that building continuing (or projecting) over the pergola, so the two structures essentially share the same roof. Whether your new pergola is attached to your home or is a free-standing structure, what kind of roof should it have? This largely depends on the local climate.
Fixed, Solid Roof
It's well-known that predicting the weather isn't an exact science, however, you'll have a good idea of the typical weather conditions that your pergola will have to face each season. In areas susceptible to rain, whether torrential or not, a fixed, solid roof can offer the most protection. It also offers substantial protection from the sun, and the end result won't require much in the way of maintenance.
Fixed, Adjustable Roof
If the weather truly is unpredictable in your neck of the woods, consider a pergola with a fixed, adjustable roof. The design of such a roof can vary, and pergola builders can offer you a number of different choices. An adjustable pergola roof is generally a panelled roof, and each individual panel can be tilted to open the roof, allowing you to control the amount of shade. Opt for a motorised roof so that you don't have to get up to manually adjust the panels as the sun moves across the sky. A downside to adjustable panel roofing is that when the panels are closed, the seal is not quite watertight, so a small amount of rain can still drip from the ceiling. This isn't exactly a major problem, since you're unlikely to find yourself sitting in your pergola in the pouring rain.
A canopy roof is when the gazebo is completed with the addition of a shade sail to serve as its roof. Although this is a cost-effective and stylish option, you need to be cautious about the nature of the fabric. It needs to be high-grade architectural shade mesh for maximum longevity and UV protection. Low-grade, inexpensive shade sails have a much shorter lifespan and will need to be replaced after a few years. A canopy roof can be fixed or retractable, which again, allows you to regulate the amount of sunlight in the pergola.
You'll be spoilt for choice with the number of different pergola roof styles, but the local climate should play a major role in your decision.