Sugar is an oft-misunderstood ingredient in dough. Some people believe that it's necessary to include sugar to feed the yeast. In truth, yeast is perfectly happy munching on flour. If you don't want to add sugar, you don't have to, and there are plenty of breads where sugar is completely unnecessary.
On the other hand, sugar plays several roles in dough besides that of yeast-food. Like salt, it's a flavor enhancer. White sugar, honey, brown sugar and all the other variations add their own subtle flavor to bread. Which one is absolutely right for a loaf of bread depends on what you're looking for, and fortunately, you can usually substitute any sugar for any other in bread recipes. Of course, the results won't be exactly the same, but things won't go horribly wrong.
Sugar is hygroscopic, which means that it attracts and retains moisture. Add too much sugar it will compete for water with both your yeast and your flour. Yeast will become less active, and it'll be tough to get gluten to develop in your dough. Because of this, very sweet doughs sometimes use extra yeast and require more kneading. Some will even call for extra gluten to be added.
Sugar helps create a fine crumb and also tenderizes dough, making it more extensible. In large amounts it can over-tenderize to the point where the gluten structure collapses. Sugar also promotes browning, and in larger amounts improves the shelf life of the bread product. Corn syrup in particular helps retain moisture and staves off staling, which is why it's such a common ingredient in shelf-stable supermarket breads.
Chances are that you aren't making super-sweet pizza dough, so you won't be using large enough quantities to cause adverse reactions, but it's something to keep in mind for bread doughs.
Types of Sweeteners
There are a few things to consider before you substitute one form of sugar for another. In a recipe that uses just a little sweetener, there's no problem substituting a wet sugar—like honey or agave—for a dry sugar. The small amount of extra moisture isn't going to throw the recipe out of whack. But in a sweet dough, substituting wet for dry or dry for wet will affect the hydration. It can be compensated for, but it's something to keep in mind.
Many bread recipes call for white sugar. It's cheap and easy and doesn't add much flavor except pure sweetness. Raw cane sugar and brown sugar add a little more flavor and color. They also contain trace minerals not found in refined white sugar.
Cane syrup and molasses add even more flavor, color, and trace minerals. Whether it's appropriate for your dough is up to you. Molasses contains a naturally-occurring acid, and that acid is also present in a smaller degree in brown sugar (most commercial brands are made by mixing white sugar with molasses). Whether the extra minerals and the acid in molasses and brown (or less refined) sugars have any effect on dough is up for debate. Their greater impact is on taste.
Agave nectar comes in a variety of grades, from very light, neutral flavored syrups, to darker, more full-bodied flavors. It is thinner than molasses or honey, so in larger quantities you'd need to adjust hydration even more. Unlike honey, it doesn't crystallize when stored.
Honey creates a more golden crust than sugar does. It also helps to keep bread moist and adds a distinctive flavor. Because of its antibacterial properties, it retards mold, which improves the shelf life of baked products. But that antibacterial property has a downside—some honeys can kill yeast. I've found that this is a rare occurrence, so it doesn't keep me from using honey. But it does mean that every time I open a new jar of honey, I use it to proof some yeast so I know it will be safe to use in all my yeast-risen doughs.
Honey powder is a fine power, somewhere between powdered sugar and granulated sugar. Since it's dry, there's no need to worry about adjusting for moisture content and it's easier to measure than liquid honey. You can find this at spice shops and online.
Similar to honey powder, I found honey crystals at an Asian market. They are small round balls that taste like honey, but the ingredient list also includes cane sugar.
While not a sugar itself, diastatic malt (malted barley flour) converts starch to sugar and helps feed yeast. It also adds a distinctive flavor. This malt has active enzymes that affect the texture of dough. A little bit goes a long way—too much of it will result in a sticky, gummy bread and an overbrowned crust.
The other malt, non-diastatic malt (barley malt syrup or malt powder) just adds flavor and sweetness. It doesn't covert the starch the way diastatic malt does, and it's not hygroscopic like sugar, so it has a lot less effect on the dough than other sweeteners. It does have a distinctive taste, however, which might not be appropriate in all recipes. It's pretty good in a milkshake, though.