Do seeds go off?

It depends on what the seed is!  Some things will still be viable after a decade; others need planting the same autumn they're harvested.  There's a list of vegetable seeds somewhere in the articles on this site.  Even if they're something that the viability drops off, you'll lose nothing by bunging them in somewhere, so long as you still have time to resow later if they do fail.

Thanks -most of my seeds seem to be viable according to the linky ou sent me -despite the plant date being much shorter on the packet. I suppose its like best before dates on food!

The life of seeds also depends on how they are stored - in the greenhouse getting cooked or outside getting damp shortens the life drastically.

Best place for left over seeds is in a air-tight box in the fridge
 
most will last for last for years past the 'sow by' date although germination levels may drop -you could just sow a few more.

With the price of seeds it's worth hanging on to the left overs

http://www.allotment-garden.org/vegetable/general/seed-storage-life.php. This will give you an idea on how long they are viable.

Thankns for pointing me towards this Val -- I shall sow my elderly radish seed with confidence later this week (eaten all the first lot and second lot on the way -- need more supplies to bribe the children with  as an awful lot of lettuce to transplant