Some languages, like Chinese, don't use whitespace to separate words at all.
Other languages will use punctuation differently - an apostrophe might or might not be a part of a word, for instance.
Case-folding rules vary from language to language.
Stopwords and stemming are different between languauges (though I guess I'm straying from tokenizer to analyzer here).
Edit by Bjerva: Additionally, many languages concatenate compound nouns. Whether this should be tokenised to several tokens or not can not be easily determined using only whitespace.