A zero-fee transaction will still get confirmed, although it may take a day or so. Although this is certainly longer than it used be as mining gets more commercialized, this really shouldn't be the case since the 25BTC reward overwhelms current transaction fees so miners shouldn't care. It's anyway a good habit to give a fee because this is the only way Bitcoin can work long term.
In fact, it could take more than a day... According to what i have read, it could actually take even more than 3 days to be fully processed.