Assuming that there is always a single space between day and month use this formula - data (e.g., 10 11) in cell A1 and formula in cell B1
=DATE("2010",RIGHT(A1,LEN(A1)-FIND(" ",A1)),LEFT(A1,FIND(" ",A1)-1))
You will need to change the hardcoded year as required.
Format cell B1 with a date format (Right-click, select Format Cells... then Numbers Tab and select an option under Date or use a custom format - if you just want day and month try "dd/mm" for 10/11 or "mmmm dd" for November 10)
Drag the formula down alongside your dates. Stop when year changes and change the year in the formula and drag the revised formula down again.
After formatting as you want, you could Copy - Paste Special - Values and Number Formats.
Then you get rid of the formulas and can erase your original column of dates.
Doing the above gives you 'real' Excel dates that can be manipulated further such as extracting data for a range of dates, or calculating number of days between dates.
Here are my test results:
1 10 11 10-Nov-2010
2 1 2 01-Feb-2010
3 20 1 20-Jan-2010