Well in terms of your offline wallet i think it is anonymous but if your talking about online wallets and moving bitcoins, cashing them, buying items with them then you lose that anonymity.

http://www.pcworld.com/article/2047608/bitcoin-offers-privacy-as-long-as-you-dont-cash-out-or-spend-it.html
http://www.businessweek.com/articles/2013-08-27/bitcoin-may-not-be-so-anonymous-after-all