If using bamboo skewers, soak skewers in cold water at least 30 minutes to prevent burning. Prepare outdoor grill for direct grilling on high.
In large bowl, combine brown sugar, chile powder, paprika, cumin, cayenne, 1/4 teaspoon salt, and 1/4 teaspoon freshly ground black pepper. Add shrimp, peaches, and onion; toss until evenly coated.
Thread shrimp, peaches, and onion alternately onto skewers.
Grill 3 to 4 minutes or until browned and shrimp just become opaque throughout, turning once. Serve with lime wedges.