I think you just run a higher risk of them being moldy past the Best By date. Seals and bags aren't meant to last forever, and over time moisture could seep in and cause mold. I think another issue you would run into, particularly with a cake mix is possible loss of strength of the leavening agents.
I work at a grocery store and I usually explain it this way (as this was how it was explained to me)
Expiration date or Use by date: exactly as it says, you typically find this on highly perishable items and it tends to be the safest bet to just discontinue use of these items on this date.
Best by date: The product will start losing flavor/quality/potency after this date. For this product to be at it's "best", it should be used before this date. It's typically safe for a little while after the date, but you will probably find it will react/taste a little differently than it would when it's fresh. How long you can keep a product past it's best by date depends on the product.
Sell by date: I deal the most with these dates. The sell by date is the last day I can sell a product, knowing that it will still be good in the time it should take you to go through it, or the bulk of it. If I have a product with a sell by date of 2-19-11, and I sell it to you, depending what it is, you'll still have time to use it. If I don't sell that product by that date, I have to get rid of it. Again, that window of use is going to depend on the product itself.