A good synonym for notorious is infamous; both words mean "well-known, and not in a good way." A celebrity convicted of a series of crimes might be referred to as notorious, as might a book that has been banned in several countries. The word originally meant just "famous" and could carry either positive or negative connotations. Only in recent centuries did the negative uses start to outweigh the positive ones. In general, you'd rather be famous than notorious, unless you're looking to build a bad reputation.