Are you sure that you are no logged in to your Google account in Firefox (Google promotes visited sites)? Additionally you may has a different browser language.
I’m GNU/Linux user and currently I have installed two browsers Firefox and Chromium (Chrome equivalent) and in both the result is same. Please check the request headers (especially field Accept-Language), you could also try to clear the cookies.
The first is the COM page, because my Accept-Language is EN.
To check headers you can use Firebug in FF, or dev tools for IE9 [key F12], and Inspect element/NET tab feature for Chrome. I never used Opera so you have to find out yourself how to check this.
I see that you’re from Denmark so probably some browsers use your system default (local) settings to conclude the headers.
Similar situation happens with systems and encoding, my default encoding on GNU/Linux is UTF-8 but Windows use Windows-1250 (if I remember well). No matter, that I’m using the same browser. Browsers just use system local settings.
There are local settings like language, timezone, etc. some browsers may shares these setting with operating system.
The Google results may be vary in case of vary request headers not a browser, but yes request headers may be dependent on browser and platform.
Enable firebug, and go to the Net tab. Reload the page and go to the HTML (or ALL) sub-tab and then click plus sign next to GET http://www.google.com/search?q=alphaville in a request list. You will see two tables Response Headers and Request Headers (this is the one).
I noticed that also. I am using chrome and my office neighbor is using firefox. I told him to search for a word in google to show him something but the results were different from my search. So, yes, the results are different.