Back in January, the big news was that a freeze in Florida had destroyed much of their crops. No biggie. They'll just import more from Mexico. And then the freeze hit Mexico and was so bad that it even took their greenhouse crops.
They say this could affect produce like green beans, eggplant, and asparagus. The hardest hit is expected to be on cucumbers, various squashes and peppers, and tomatoes. There's no panic expected here, but they do expect prices to go up significantly until they can re-grow the crops which could take as little as 60-90 days. In the meantime, we could expect that prices will go up on cucumbers, squashes, green beans, and tomatoes...all favorites that are frequently used at our house.
You can't do much about the fresh produce. If you want it, you'll have to pay the temporarily increased prices. However, you CAN take fresh produce that you get now and preserve it so you at least have that produce in a fresh-frozen form to use in cooking.
I actually do this a lot and it takes very little time and no special tools!
My favorite things to pre-dice are onions and bell peppers. I cut them as soon as I get them and toss them in the freezer in small baggies. When I am in a hurry but want the "fresh" produce, they're ready to go...and don't require any pre-processing!
Any other produce will require blanching before freezing, but that is incredibly simple. You cut the produce as you want it (shredded, diced, etc). Once the produce is cut, you throw it in a pot of boiling water. After boiling for the required amount of time, you submerge the veggies in ice water to stop the cooking process. Once that's done, you freeze. This gives you fresh-tasting veggies from the freezer. The "Southern Food" section of About.com gives detailed instructions on freezing just about any vegetable.
You can use glass jars to freeze things in (be sure to leave an inch of head space or empty room) or you can use baggies. (You can freeze them in portion-sized small baggies then put those small baggies in a gallon freezer bag to prevent freezer burn.)
This can not only help you keep those veggies in stock even if prices go higher for a bit, but will also save you time on prep later!