By and large, languages have rules, and exceptions are--well, the exception. Exceptions tend to occur more often in common words (perhaps because children don't learn the exceptions in rare words, unless they're drilled on them--which we do on English in school). One question though is where the boundary is between rule and exception. In Spanish, various subsets of verbs undergo stem allomorphy. This can generally be described as rules (you do have to know which words undergo those rules), but it's unclear where the rules stop being rules and start being exceptions.

Also, while there are often exceptions in morphology, exceptions are almost non-existent in syntax. Again, much depends on where (or whether) there is a distinction between rules and exceptions. In English, unlike some languages, adpositions go before the NP (hence their name, prepositions). But there is at least one English adposition that follows the NP, namely 'ago' (hence it is a postposition). Is this an exception? Depends on your notion of "rule".

Also BTW, the line between spoken and written language isn't really a question of writing, odd as that may seem. Transcribed speech is still an oral language, distinct in many ways from written speech (e.g. written speech, even in newly written languages, tends to be syntactically and often lexically more complex than oral speech in the same language).