There's no way to have a date without a year, it's simply a required part of a date. Just like the second is a required part of the time of day - if you enter, say, "1:15", the actual value will be "01:15:00" (or something like that, depending on your regional settings). The only thing you can do is format the column as text, use a date format that hides the year, or tricks like using formulae to extract the day and month into another column and hiding the column with the actual date.
Excel stores dates as the number of days since 0 (yes, zeroeth) January 1900. So today, 23 August 2012, would be stored as 41144, and 23 August 2008 would be stored as 39683. Because of this, Excel needs to know the year in order to calculate the correct number of days. 23 August on its own is ambiguous, because it could resolve to over 100 different values (one for each year since 1900), that's why Excel adds the year itself if you omit it.
For the time of day, Excel appends a fractional part to the number of days, which represents the fraction of the 24-hour day that has elapsed. For example, 06:00 (or 6 AM) is stored as 0.25, because at that point 25% of the day has passed.
You can see this in action by entering a date and/or time (or just
=NOW() for the current date/time) into a cell in Excel and changing the format to Number. You'll also have to increase the number of decimal places to see the full precision.
For example, the current time (20:19 in my timezone, as of the writing of this) is stored as 41144.846945255.