Excel's date format without a year

Short answer:
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.

Explanation:
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.

Might need to use a few steps.

You have the full date. In a column beside it, place the following formula.

=CONCATENATE(MONTH(A1),"-",DAY(A1))

This will give you the month, a dash, the day. You may want to pretty it up, or use multiple columns.

Then, copy all of the cells with the new month-day combination.

In the next column, Paste Special, and select Values. This will create new cells without the formulas, just the values in the end.

Finally, delete the columns with the original date, and the formula from above.

As far as I know, this isn't possible. You can format the cell as mm/dd but if it's a date, it has 3 parts: month, day, and year. Excel will add the year for you when you enter just the month and day. You will see it as mm/dd but since a date by definition has to have a year in it to perform date arithmetic, you don't have a choice really. The only way I can think doing this is formatting it as a text field. But you will lose the benefits of the data format. What do you need this, may I ask? In most cases you can avoid using the year in your arithmetic if it bothers you.