Basque

When the British Foreign Office conducted a serious survey about the same matter as this post, Basque was one of the first languages they came up with. The language has 24 cases, no links to any other Indo-European language and is extremely agglutinative. This means that they take a few simpler words, add prefixes and suffixes as and where they can to make a new complicated word out of the simpler old ones. 

Moreover, it is synthetic rather than analytic besides having many more moods than other European languages. Couple all of that with its complex system of denoting a subject, direct object and indirect object (they're all crammed into the verb itself) and you've got yourself a mighty compacted language to learn indeed!

-Picture courtesy thinkstock-