There absolutely are dates.
I'll tell you how to find the dates on the API kits and the Saliferts because that's what I have in front of me at the moment.
API:
Each bottle is printed with a Lot # right above the label. For example:
My High Range pH bottle is printed: LOT 27A1009
This means that it was made in 10/09. Which also means it's expired. I guess it's time to go look at the rest of my test kits. Great, see what you started! LOL
Salifert:
Each bottle that comes with the test kit will be printed with a batch number. For example:
My calcium kit bottle 3 (ca-3) is printed batch: 0410-A This means that it was made in 04/10.
The Ca-2 is batch 0310-E and the Ca-1 is batch 0310-M, which means they were made in 03/10. You want each bottle in the test kit to be similar in when they were made. A month won't make a difference, but more than that can.
There is also a way to tell on the SeaChem kits and the Elos kits, but I don't have them in front of me right now.
Also, Red Sea Pro Individual test kits (which I don't recommend) have a exp. date stamped into the cardboard box that they come in, usually with month and year.