No matter how brilliant, your tweets just aren't copyright material, writes Jeffrey Zeldman. The law covers "fixed phrases," but that doesn't apply to names, titles, or short phrases. At 140 characters max, tweets are most definitely in the latter category, making them fair game in the public domain. At best, you can try to trademark one. "Good luck with that."
"However original, witty, or profound they may be, nothing more than good manners protects your original expression of authorship," he explains at Zeldman.com. "If this disturbs you, suck it up, or stop using Twitter—or mark your Twitter feed as private. This will not copyright your Twitter mutterings but it will keep many people from seeing them."