I do NOT know how effective the glass jars would be, but I would grow basil, oregano, mint... basically anything from the herb section. Useful, yummy, easy to grow...

How about some sprouts?

The 'Classico' jars are actually Mason and Atlas "canning jars" that can be used to can vegetables, fruit or jams & jellies.

A little tricky growing things in containers without drainage holes - watering "just the right amount" is tricky even for experienced gardeners.
Best use might be for rooting cuttings.....

terrariums? http://www.re-nest.com/re-nest/roundup/10-uses-for-mason-jars-147943

I grow clover in a sealed jar terrarium on my windowsill. Too bad we don't eat clover, so there's not much practical use for it. Every once in a while, I'll feed a bit to my pet rats, but for the most part, it's just for looks.

The good thing about jars is that you can see the moisture of the soil below the surface, making it easier to water the right amount, as opposed to an opaque pot. Everyone says not to grow plants in containers with no drainage, but I typically either have the same luck either way or my plants in non-draining containers thrive while the plants in pots with holes tend to slowly wither.

I'd go with small plants, terrarium-style. They're really easy to make, and almost self-sufficient.

Since there is no drainage, I would stick with plants that you don't need to water often like succulents. Add stones to the bottom of the jar and then plant the succulent in course soil.

Otherwise, you can skip the soil altogether and plant in just a jar of water. Plants that will grow in water are certain types of bamboo, lilies, and ivy. You may need to use stones in the bottom of the jar with this method, too. You also may need to support the plant with a lid or plate (with a hole in it) on the top of the jar.

My brother claims he put some lemongrass in a jar with water and that it is thriving.

Brew kombucha tea in a glass container covered with muslin (to keep out flies). Give it as holiday gifts in those nice glass containers. All you need are the kombucha 'mother', tea, sugar and clean water.

I have grown cat grass in those exact jars, use them for succulents and terrariums as others have mentioned. If the mouth of the Jar is wide enough you could use them for starter seeds, lightly water them, put the lid on and put in a sunny window. It will create its own moisture and need very little water. Since they are mason jars you can use them to make small batched of ice tea, they wont shatter when you pour hot water in. I use jars with lids as cups.

http://www.ehow.com/list_5805271_plants-grow-jar-water.html

RE: the drainage issue - you can successfully grow all kinds of plants in containers without drainage so long as you put a layer of gravel and/or sand in the bottom. This allows the water to drain out of the soil so you don't rot the roots off of your plant. Another great thing about using glass jars is you could easily see whether or not your plant needed more watering and you know exactly when the plant has gotten too big for the jar (roots will start pressing and tangling against the sides).

If I didn't use my pb and spaghetti sauce jars for food storage (leftovers, grains, dried beans, homemade fridge jam, applesauce) I would totally try this!