Different airlines have different polices on this. First of all, Hilmar's advice to check SeatGuru first is good advice. If you find there that the seats are narrower than your hips, you do have a few options, depending on airline and route.
International Premium Cabins
On large aircraft configured for long-haul routes, there will usually be Business and/or First-Class cabins that have quite spacious seats (most of which recline fully in to beds these days.) These are usually at least 20 inches (51 cm) wide, sometimes significantly more. Granted, they're typically not cheap.
Domestic/Regional Premium Cabins
For aircraft configured for short-haul (e.g. domestic, regional, or intra-Europe routes,) there are often still premium cabins, but they're not nearly as spacious (or expensive) as the ones you'll find on long-haul routes. In North America, these are typically called "First Class" and are significantly wider seats than what's installed in economy. In Europe, they're typically called "business class," and are the same width as what's installed in economy, but with the middle seat blocked off.
There's less variation from short-haul to long-haul in the dimensions of economy seats than with the premium cabins. They're typically 17-18 inches (43-46 cm) wide on either short-haul or long-haul. Some very-low-cost airlines even have a 16-16.5 inches (40-42 cm). However, many airlines have policies allowing you to book the seat beside you, sometimes for free.
According to this article and this article, here are the policies of some North American airlines (I don't personally know how these vary in Europe.)
Free Extra Seat
Extra Seat Cost Reimbursed if Flight(s) Not Full
Must Pay for Extra Seat
Will Seat Next to Empty Seat Free if Available, but Recommends Purchasing Extra Seat