Seattle is generally safe. For many visitors the most menacing presence are the panhandlers who tend to frequent Pioneer Square, Belltown, Capitol Hill, the U-District, and some area parks. Even visitors and transplants who come from other major cities with large homeless populations are surprised by how aggressive (and at times, verbally abusive) Seattle's panhandlers can be. You may pass your entire vacation without incident, but don't be surprised if someone curses you out after you refuse to give them money.
The airport, ground transit links, ferries, and popular sights are well monitored by guards and cameras, and the city's knowledgeable travel personnel are on hand to help set visitors in the right direction. Tight rules apply as to what you can bring into stadiums, arenas, and performance venues; expect bag searches, X-ray machines, and/or metal detectors.
Use common sense and you'll avoid trouble. Always lock your car (there are plenty of break-ins, especially in residential areas), don't leave valuables in your vehicle, and park in lighted areas after dark; be careful when walking alone Downtown during late hours; don't flash cash or valuables in heavily visited areas where petty theft might occur. Keep your laptop in the hotel safe when you're not using it.