It's easy to make vegan bread.
In any recipe, you can substitute your favorite vegetable oil for butter,
or substitute applesauce for the oil. If you don't use *any* oil, the
bread is more crumb-y, so using 1/2 oil and 1/2 applesauce is a good mix.
We use 1 TBSP oil and 1 TBSP applesauce for 3 1/2 cups of flour in our
large machine.
You can also just leave out the egg, and substitute a TBSP of water or
other liquid for each egg. There are also vegetarian egg substitutes; I
don't know much about them but I think they are based on lecithin. Again,
leaving out the egg makes the bread less 'cake-y' and makes it rise less.
Whole wheat sandwhich bread doesn't need eggs, but cake-like breads
(cinnamon bread, challah, fruit breads) will suffer a bit.
Don't put too much extra weight (raisins, nuts, other stuff) into a bread
without egg. A pinch of baking soda can help heavy breads, at some
nutritional cost. Egg also helps "glue" the loaf together; breads with
lots of mushy ingredients, like carrot bread, are most likely to suffer.
We've made excellent banana bread without egg.
You *can't* leave out sugar completely. The yeast *eats* the sugar which
causes the bread to rise. You *can* substitute honey or sucanat (lightly
processed natural brown sugar) instead of white sugar. You can also usually
use about 1/2 the sugar that most recipes call . If you substitute honey
for sugar, decrease the water in the recipe by about 1/2 the amount of
honey (ie if you use two TBSP honey, instead of 1/4 cup white sugar, cut
the water by 1 TBSP)
Note: you'll have to experiment with quantities of water.