This article is a travel topic
English is very much a world language — it is taught as a second language in many places — and it is possible to travel almost anywhere using only English.
Nearly anywhere, if you stay in heavily-touristed areas and pay for a good hotel, enough of the staff will speak English to make your trip painless. Nearly anywhere, you can hire an English-speaking guide and translator--especially if you take care of it beforehand. Travelling this way may not be as cheap or as interesting as it could be, but it will be relatively easy.
For a business trip, paying for good hotels and guides or translators may be the best strategy; the convenience and ability to get things done are more important than cost. For a backpacker on a tight budget, this is generally not a good strategy; coping with language difficulties is part of the adventure. Many travellers fall somewhere between; they may choose a hotel where English is spoken, but they will also have linguistic adventures in the markets.
In many areas, it is very useful to learn some of a regional language. This is generally easier than trying to learn several local languages and is more widely useful. Even in really out-of-the-way places, you should at least be able to find hotel staff and guides who speak the regional language well.
Regional languages that are used in many countries are Russian for Central Asia and the Caucasus, Arabic for the Middle East and North Africa, French for parts of Europe and Africa, and Spanish for most of Latin America. Other languages such as Portuguese, Mandarin, Hindi, German, Persian, and Swahili are important for particular areas.
Regional languages are often useful somewhat beyond the borders of their region. Some Russian is spoken in Northern China, some German in Turkey, and so on.
Coping without a language
There are several ways to cope with travel in countries where English is not spoken:
Widely used expressions
A few English words may be understood anywhere, though which ones will vary from place to place. For example, "OK" and "bye-bye" are used in Chinese and many Chinese speakers also know "hello" and "thank you". Unless you are dealing with educated people, however, that may well be the extent of their English.
French words also turn up in other languages. "Merci" is one way to say "thank you" in Persian.
English idioms may also be borrowed. "ta-ta" is common in India, for example.
Abbreviations like CD and DVD are often the same in other languages. "WC" for toilet seems to be widely used, both in English and on signs, in various countries, though never in English-speaking ones.
Words from the tourist trade, such as hotel, taxi and menu, may be understood by people in that line of work, even if they speak no other English.
Some words have related forms across the Muslim world.
Even if you use the form from another language, you might still be understood.
Some loanwords may be very similar in a number of languages. For example, "sauna" (originally from Finnish) sounds similar in Chinese and English among other languages. Naan is Persian for bread; it used in several Indian languages, though the recipe varies.
The word for tea is approximately "chai" across most of Asia (Hindi, Russian, Persian, Turkish, ...), "cha" in standard Mandarin and Cantonese (albeit with different tones) and "teh" in the Minnan dialect (in fact, the English word tea was derived from teh).