Immediately after posting this suggestion, I came across an existing API for the tinyurl service. Rather than repeating the code here, I will reference the page where it can be found...

http://www.richardcastera.com/blog/creating-a-tinyurl-with-tinyurl-api

Addition to Solution 1:
It would be nice if the value of SHORTSURVEYURL could also be displayed on the survey overview page under "Survey URL" or (if no short survey url exists) a link/button for creating a short url for the survey.

With respect for the good ideas of vierundzwanzig, it doesn't make sense to display the SHORTSURVEYURL on the overview page as suggested; because the SHORTSURVEYURL should be generated from the complete URL, including the "token=xxxx" clause specific to a particular invitation.

The Survey URL (lang) shown on the survey overview page is only a partial URL (it doesn't contain the "token=xxxx" portion of the complete URL), and is not equivalent to the string substitution variable SURVEYURL.

Since tinyurl will be used to compress the entire URL (including the "token=xxxx" clause), any short URL generated without this information will be meaningless.

Using build 11379 as a starting point, I have written all the code necessary to implement this idea. I just need to create the "deltas" for the updated modules so it can be easily submitted to LimeSurvey for inclusion/testing.

The modules affected are as follows:

common_functions.php - add new function getshorturl

fck_LimeReplacementFields.php - added new items to dropdown list of available user substitution variables

register.php, tokens.php, lsrc.help.php - added code to each module to define the replacement strings for new tokens:
SHORTSURVEYURL and SHORTOPTOUTURL

The only thing I did not do is to check whether there is a translation function change needed to make the new UI strings:

"Short URL of the survey" and
"Short URL for a respondent to opt-out this survey"
available in a language other than English.

Now that I've upgraded my installation to the latest build, I've been able to test my code. There are errors in the HTML generated tokens (stupid mistake) which I am working on correcting.

I'll post an updated zip file when I've fixed the problem.

Errors have all been corrected and the feature works perfectly. I will be uploading the code change for hopeful inclusion in the trunk.

I have uploaded a zipfile containing the patched programs that implement the current idea. You can find them here:

http://www.limesurvey.org/forum/future-features/69878-ability-to-call-a-url-shortening-service-when-generating-invitation-emails?limit=10&start=10&lang=en#70377

If someone on the development team wishes to verify that this patch works, maybe you would consider adding it to the trunk.

(I also corrected an error in line 159 of the original register.php file - the "?" was missing between the "optout.php" module name and the first input parameter).

@JEfromCanada:
If you don't use tokens (e.g. for an anonymous survey) it makes sense. Perhaps a new variable like SHORTURLENTIRESURVEY that just shortens the general survey url (e.g. http://localhost/limesurvey/index.php?sid=28815&lang=de) will help to solve this problem.

I've created a user patch in the bug tracker system:

#5621