Part of the answer depends on whether or not you are going to be feeding the year into some other calculation.
If you need the actual 4-digit year in the cell, and no other numbers in that cell, you can use either =year(today()) or =year(now()) as the formula in the cell, and make sure the format of the cell is either "Numbers" tab | Category:Number | Format:General or Format:-1234. (A cell that hasn't been formatted has the formatting code of "Numbers" tab | Category:Number | Format:General.)
If you just need to display the current date as a 4-digit year and you don't care what the cell really contains, you can do the above to get the 4-digit year, or you can put the date in the cell (using =today(), or if you want to include seconds, =now() as the formula for the cell) and then format the cell to display as "Numbers" tab | Category:Date | Format: custom format code: YYYY (four upper-case Y's).
What will not work is to get the year into the cell by =year(today()) and then use the "Numbers" tab | Category:Date | one of the mm/dd/yyyy formats because then the cell has the year but the formatting routine for displaying that cell's value thinks the cell should be interpreted as if it had a date serial number, and 2013, for example, as July 5, 1905.
So, either extract the year (=year(today()) or =year(now()) to get just the year) and display that as a number, or get the date via =today() or =now() and display that value as a custom date format of YYYY.
