Among European countries, English is the primary native language only in the U.K. and Ireland, but it is widely spoken as a second language elsewhere. In Nordic countries and the Netherlands, a large portion of the population speaks English well, even in smaller towns. In Western Europe, you won’t have much trouble finding English speakers in major towns or popular tourist sites, and most people who work in the tourism industry speak English.
The farther east you go, however, the less English you’ll encounter (though hotel staff still commonly speak English). English speakers can certainly still travel in those countries, it just might be a bit more challenging.