Firstly, Thanks Frank it works like a dream.
=SUMPRODUCT(--(B1:B100<""),--(A1:A100<""),--(B1:B100<=TODAY()))

I thought I could work the rest by myself but I have another question.

I am now trying to add up the number of rows which have date entries from
two columns, which using the current date is on or after column B and before
or on column C, and only if there is an entry on the same row in another
specified column A.

for example
A B c
1 x 12/12/2004 14/12/2005
2
3 r 10/10/2004 12/12/2004
4 t

The total for this would be 1 (row 3)

Many Thanks again