The addresses are pseudonymous. That means that any anonymity attached to them is fragile.
If you interact with entities that also re-use addresses: like a bitcoin accepting business using one address, people may learn that you frequent said business just by looking at the block-chain. This is not like the traditional banking system where most things are kept private by default (for fear of identity fraud, among other things).
There are ways to mitigate that though:
CoinJoin: Bitcoin privacy for the real world