Tax fraud and organised crime aside I'd say getting into the online music business. Staying anonymous for as long as possible today probably is the only way to establish an independent business in that industry without having to pay extortionate licence fees to the big four.
Disagree regarding the music business. They don't care if the owners are anonymous, they'll go right after the LLC itself and destroy it as necessary, while trying to pierce the anonymous aspect any way they can. Having an anon-ownership list won't protect the company from their licensing fees at all.
