I agree that in most countries you should be OK even without knowing a local language, but I think you miss out on a lot particularly when lots of people don't speak English. In countries like the Netherlands or Norway you can probably rely on a majority of people knowing some or a lot of English and often many signs are also translated.

I took a year of Spanish at university so my skills are not the greatest, but when I visit the country I can go into all sorts of small shops/cafes etc and be understood by non-English speakers, I have also been able to ask for directions when I got lost and get help from non-English speakers. And also in some less visited tourist attractions I was able to read information boards that were not translated, whereas my German is not good enough to do this in Germany. Spain is the only European country where people in the tourist industry initially try to speak English to me but when I respond in their language they actually seem relieved.

On the other hand because I want to know some of the language before I visit a country, I have been reluctant to visit places such as Eastern Europe due to lack of time to study; but it turned out that I had to go to many of these countries for business reasons anyway and I felt that I could have got a lot more out of my visits if I had been able to learn some Slavic.