Speaking as a translator, I can share a few rules of thumb that are popular in our profession:
- Hebrew texts are usually shorter than their English equivalents by approximately 1/3.
- Spanish and Portuguese texts are longer than their English counterparts by about 1/5 to 1/4.
- Scandinavian languages are pretty much on par with English. Swedish is a tiny bit more compact.
- Whether or not Russian is more compact than English is subject to heated debate, and if you ask five people, you'll be presented with six different opinions. However, everybody seems to agree that the difference is just a few percent, whether this way or the other.
So much for complete texts, on average, as a rule of thumb. Obviously, when you are working on a GUI, you mostly have to deal with translating individual words, which changes the picture dramatically. I am not aware of any universal research on the subject, but I will actually go out on a limb and say that it would be worthless to you, precisely because of being universal.
First of all, let's have a look at English itself. A very popular estimate for the average length of English words is 5 letters (or 5.2, or 5.3, or 5.1). I will not expressly address the validity of that estimate here, though I will link to this tiny bit of intriguing research. Much rather, I will focus on saying that your mileage will always vary.
It all depends on what application you are writing, and for which target audience. You might be writing a text editor for children, a web browser for everyone, or a worst-case execution time analyzer for the aerospace industry. Sometimes, your menu entries will read "Open", "Edit", "Save" and "Quit". Other times, they will read "Crossing reduction" and "Simulated annealing". Add into the equation that "Quit" is not necessarily short in all languages, and "simulated annealing" is not necessarily long, and you've got yourself a complete mess, no matter what the universal research says.
Secondly, there is something to be said about the units in which one measures the average word/text length. Traditional research and urban legends alike usually focus on the number of letters. But for a GUI designer, that kind of information is rather useless, because he measures the screen real estate in pixels.
As a simple example, in terms of letters, "貓" is 66% shorter than "cat" (which is what it means) and 75% shorter than "neko" (which is its Kun reading). But in terms of pixels, you don't save anywhere as much space. So, whether or not your menu items in Japanese, Chinese, Arabic, Farsi or Urdu will end up being shorter than their English counterparts depends on how you define "shorter".
The tricky part is that to one extent or another, this is true for every pair of languages, even for those that use the same alphabet. You have the English word "illicitly", and you translate it into Phantasese, and you get "mamwowo". Now what? It's two letters shorter, yet it no longer fits. (Unless, of course, you are using monospaced fonts everywhere, which is highly unlikely.)
Lastly, I would like to specifically address the myth that German words are oh-so-long. All those awfully long German words are only that long because they correspond to many words in other languages. "Kontrollflußgraphvisualisierungssoftware" is no longer than its English counterpart, "control flow graph visualization software", and the famous "Donaudampfschiffahrtselektrizitätenhauptbetriebswerkbauunterbeamtengesellschaft" is considerably shorter than its English translation. Yep, you heard that right, that monster of a word actually saves space. German words can be long and succinct at the same time, and English recognizes that by borrowing (kindergarten, wunderkind, doppelganger, wanderlust, zeitgeist, schadenfreude...).
Edit: I want to add that when it comes to GUIs (or news headlines), English loves to cheat by dropping articles. "Export file" rather than "export the file", "import image" rather than "import an image", and so forth. Many languages can't do that because they don't have articles to begin with. If there's any advantage Russian does have over English in normal prose, it's not having "a"s, "an"s, "the"s (and "to"s) scattered all over the place. When it comes to GUIs, Russian loses that advantage, and an English expression that was longer than its Russian equivalent might suddenly become shorter. German is even better at that game: it has lots of articles to drop, none of them shorter than 3 letters, and quite a few that are 4 or 5 letters long.