In addition to the excellent node above mine explaining the differences between English and German, here is an additional pertaining to the use of case versus word order.

It was explained to me as follows:
Der Hund biss den Mann.
Den Mann biss der Hund.

Both mean "The dog bit the man", yet to the casual observer, the meaning is inversed. The former is prefered to make things easier.

The problem becomes worse when using non-masculine nouns, such as:
Die Ratte biss die Frau.
Die Frau biss die Ratte.
This is "The rat bit the woman", obviously there is no difference in the words for "the" for Frau and Ratte (both are die), therefore it is harder to discriminate. This should be resolved by context though, as it is most likely that the rat bit the girl. In this case, the second form should be discouraged as it would cause confusion.

The above examples use only the nominative and accusative cases, which are very similar, but there are other cases, most importantly in the context, the dative:
Die Frau biss die Mutter
Die Mutter biss die Frau
These are ambiguous, so SVO should be used to sort it out, but suppose the Woman didn't slap the Mother, but tripped her up (figuratively - it's the only example I can find at the moment, without changing the structure of the example too much)
Die Frau stellte der Mutter ein Bein.
Der Mutter stellte die Frau ein Bein.
The use of the dative in this sentence has removed the dependancy on word order, even though the objects are of the same gender, which caused a problem in the accusative above.

Finally, German has a lot of redundancy in it's language, I agree, but the redundancy is a way of compensating for the limits of the German class system, both are not always used, it depends on the sentence.