Fresh fruit doesn't have more sugar per piece of fruit, but the dehydration process removes so much water that it reduces the volume of each piece considerably.
For example, according to the United States Department of Agriculture's National Nutrient Database, one cup of grapes has about 104 calories, and a cup of raisins has over 434 calories. This doesn't happen because the raisin company added sugar, it happens because the raisins take up a lot less space than the fully hydrated fresh grapes. If you look at the calorie content of grapes verses raisins by pieces of fruit, then the database shows ten grapes have 34 calories and ten raisins have 16 calories.
The sugars found in dried fruit are mostly fructose and dextrose, the same sugars that are naturally found in the fresh fruit. However, some dried fruits, like cranberries, are too tart for most people to want to eat them as a snack, so sugar or fruit juices are added to them when they're dried.
Dried fruits such as raisins, dried blueberries, apple chips and dried apricots are convenient because they keep longer than fresh fruit. They're easier to carry with you than fresh fruit and it's fun to make your own trail mix with cereal, nuts and your favorite dried fruits. But yes, you do have to watch the sugar grams when you eat a lot of dried fruits.
United States Department of Agriculture - National Nutrient Database for Standard Reference Release 24. "Nutrient data for 09132, Grapes, red or green (European type, such as Thompson seedless), raw." Accessed February 06, 2012. http://ndb.nal.usda.gov/ndb/foods/show/2339.
United States Department of Agriculture - National Nutrient Database for Standard Reference Release 24. "Nutrient data for 09298, Raisins, seedless." Accessed February 06, 2012. http://ndb.nal.usda.gov/ndb/foods/show/2339.