Formula in E3:

=INDEX(A1:A10, MATCH(MIN(ABS(A1:A10-$E$1)), ABS(A1:A10-$E$1), 0)) + CTRL + SHIFT + ENTER

Download excel example file.
find-nearest-date.xls
(Excel 97-2003 Workbook *.xls)

Functions:

INDEX(array,row_num,[column_num])
Returns a value or reference of the cell at the intersection of a particular row and column, in a given range

ABS(number)
Returns the absolute value of a number, a number without its sign.

MATCH(lookup_value;lookup_array; [match_type])
Returns the relative position of an item in an array that matches a specified value

MIN(number1,[number2])
Returns the smallest number in a set of values. Ignores logical values and text