In particular, its system of declension for nouns and adjectives (and some other noun-like things) tends to drive non-native speakers batty. Wikipedia gives a good overview:
"Nouns, pronouns, adjectives, demonstratives, most numerals and other particles are declined for two grammatical numbers (singular and plural), three grammatical genders (masculine, feminine and neuter) and six grammatical cases (see below). This gives dozens of spelling combinations for most of the words, which is needed for grammatical agreement within and (often) outside the proposition. Also, there are several paradigms for each declension with numerous irregular forms."