Someone who is infamous has a very bad reputation. If you become a Hollywood star and find yourself on the pages of gossip magazines for your affairs and addictions, you will have succeeded in becoming infamous.
Infamous is from Latin infamis, for negative fame. If you're bad but unknown, then you're not infamous — it's reserved for those wicked and well-known people that capture our collective imagination. It is a strong and resonant term. Some synonyms are notorious, disgraceful, and odious. The stress is on the first syllable.