The 3,000-mile oil change interval is a holdover from the 1970s when oils degraded faster and engines were less efficient. Modern synthetic oils in modern engines often go 5,000–10,000 miles between changes.
Check your owner's manual for the manufacturer's recommended interval. Many newer vehicles specify 7,500–10,000 miles for synthetic oil.
Modern vehicles often have oil life monitors that calculate degradation based on actual driving conditions. Trust the monitor when present.
Severe service conditions (lots of short trips, towing, stop-and-go traffic, extreme temperatures) warrant shorter intervals — typically 5,000 miles instead of 7,500–10,000.
Quick-lube places push 3,000-mile changes because it's a business model, not because it's mechanically necessary.