Put the shrimp in a large ziptop bag or bowl. Add the olive oil, lime juice, salt, paprika, garlic powder and black pepper. Shake or stir to combine.
Cover and refrigerate for 15 minutes.
If using wooden skewers, soak them in water for 10 minutes prior to adding the shrimp.
Slide the shrimp onto the skewers, so they are just touching but not crowded.
Preheat a grill to 350°F (medium high heat). Oil the grill grates well.
Set the skewers on the grill and cook for 2-3 minutes per side, until pink.
Serve with parsley and lime wedges.