If you're looking to duplicate the sweetness and flavor of honey, then agave nectar is the way to go. It comes from the Blue Agave plant and tastes pretty much exactly like honey (well, no, it's better--you'll probably like it even if you don't like honey). You can find it in health food stores, or, if not, ask them to carry it. One brand is Cucamonga, which comes in light and dark flavors (packed by Western Commerce Corp. City of Industry, CA 91715-0190); another is Sweet Cactus Farms, which is a medium flavor (distributed by Original Beverage Corp. Malibu, CA 90265, (310) 838-9431). The light Cucamonga is the most like honey.
You can also get Suzanne's Just Like Honey Rice Nectar from Pangea or Vegan Essentials.
For general baking, you can substitute sugar (go for beet not cane) cup for cup and add 1/4 cup liquid per cup substituted. Or, try a sweet liquid like maple syrup, rice syrup, molasses, sorghum syrup, or barley malt. There is a liquid sweetener called Fruitsweet that is advertised as a honey replacement. All of these things have unique flavors (rice syrup in large quantities, for example, can be bitter), so you may have to experiment to find what works for a particular recipe. Honey is high in fructose, so if you are looking to replace that flavor, you can substitute fructose, which is like very sweet sugar. Corn syrup would also be good; it is extremely difficult to distinguish honey from honey that has been adulterated with corn syrup. This page has good practical information on "natural" sweeteners even if they are off on the science. See also Sweeteners for Vegans.
Whole wheat supermarket breads commonly contain honey, but you can find some that don't. Be sure to write a letter to those that do and ask them to omit the honey. If you are looking to replace honey's preservative properties for breads, agave nectar does that too (LaBell and personal experience). Another preservative is amazake, a sweetener made from koji (a Japanese rice) that has been fermented by a fungus and combined with wheat starch (Brody, B15). You can even make it yourself; I've seen instructions on packages of koji rice.
One common thing made with honey that I can think of is baklava. In the Middle East, where baklava originated, honey is not even used! The Vegan Chef has a recipe for vegan baklava. You could also try another version or some Indian baklava or or a low fat version or here's one with maple syrup (which comes from trees, not bees. Sorry.)
One thing I learned while reading all about honey was that a little alcoholic beverage called mead is made from fermented honey. I don't know how many mead addicts there are out there, but I searched for an alternative and there is something similar called pulque. It's made from, yes, agave. Before I learned about agave beer, I recommended Woodchuck hard cider.