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There are many languages which, having descended from a language with a complex case system, have lost or greatly simplified theirs: Bulgarian (Slavic), English (Germanic), most Romance languages etc. All of the above are ultimately from PIE which had a case system.
Is there an example of the opposite process: a language with a case system which has descended from a language lacking it?
In Heine and Kuteva's (2002) World Lexicon of Grammaticalization you'll find examples of words with lexical meanings "give, leave, arrive" having grammaticalized into morphemes expressing dative, ablative, and allative meanings, respectively. However, what is documented are cases of words with lexical meanings gradually changing into words which are best treated as adpositions. When you are thinking of case systems, you are probably interested in cases where a language gains a nominal affix used to express a case relation. Here, the most likely historical change is where a word which already has case-like meaning (viz. an adposition) fuses to the noun. See Lehmann (2002: 70ff.) "Thoughts on Grammaticalization" for examples.
