Availability of laundry facilities seems to vary from country to country.
In Japan, the chain budget hotels have onsite coin laundries for guests, and the Tokyu Stay apartment hotels have washer-driers in the rooms. Locals can also guide you to neighborhood laundromats.
Laundromats in the UK and Scandinavia were scarce and expensive, although I did have the unique experience of having the Zimbabwe women's BMX team help me figure out how to use the machines in Copenhagen (the world BMX championships were being held there). Interestingly enough, the otherwise expensive Hurtigrute ship in Norway had a reasonable laundry room that was available to guests.
Depending on the length of your stay, you may just want to take enough clothes to last. I once went on a 10-day group tour to a music festival in Europe, and one mother and daughter, who would be going home immediately afterwards, just packed ten days worth of clothes.
In the U.S., laundromats are relatively easy to find in large cities.