Place the shrimp into a large mixing bowl. Drizzle with olive oil and lemon juice.
Sprinkle paprika, garlic powder, onion powder, oregano, basil, salt, pepper, and cayenne pepper over shrimp. Toss to coat. Cover and refrigerate while grill preheats.
Preheat an outdoor grill to high heat, about 500 degrees F. Soak wooden skewers in water, if using, 10 minutes.
Either thread shrimp onto skewers to cook, or place the shrimp directly on the grill individually. Be sure that your shrimp are large enough to not fall through the grates if you are not threading them on a skewer.
Cook shrimp for 2 to 3 minutes per side until they are no longer translucent. Serve hot.