I've tried to learn a little about the languages where I undertake long trips (e.g. not for the weekend in Berlin, but for the month in the Spain), but sometimes I don't succeed. (My husband and I planned to study Spanish and Arabic before our honeymoon in Spain and Morocco; we managed to fit in the Spanish lessons but the Arabic fell by the wayside - something about the stress of organizing a wedding ...)
These days, I'm trying to learn Turkish because I have about 5 business trips to Turkey in the next year.
I study the language before I travel because, as other posters have mentioned, it's a great way to get a little insight into the culture of the place you're visiting, it allows you to demonstrate a little respect for the inhabitants and makes you more independent.
Have you considered incorporating language study into your trips? I've done this several times over the past few years (French and Spanish). It's not practical if you're only taking a short holiday, or only have enough time to spend a few days in each of several places - but if you've got a little time (e.g. 2 weeks for one country), it's a wonderful way to explore a place in more depth. What I've done is to take an introductory language course (e.g. 12-24 hours of classes), or use self-study guides for languages that are easier to tackle, and then sign up for a one week (one city) or two-week (two different cities) course in the country I'm visiting. The language course provides some structure to your day (e.g. it stops me from sleeping in and wasting the day), the school usually has a variety of sightseeing and social activities planned for you, you meet curious and like-minded people from around the world, and at the end of the course, you've accomplished something and are a little better equipped to go exploring on your own. Usually, you can find courses that offer 3-4 hours of instruction a day - leaving you enough time to go exploring for the rest of the day - and you can take excursions on the weekends. And if you pursue a language fairly consistently over time (e.g. 1-2 weeks of Spanish every year, in a different place), it can benefit you in your career. (I live and work in Paris now - and I got the job in part because I had brushed up on my high school French during language holidays during the past few years.)