Like rainbowgardener said the solution is to put gravel in the bottom. Something like smaller aquarium gravel would be ideal because the soil won't get washed down. But with a taller vases, you could actually do a kind of "sand art" with a layer of larger gravel on the bottom, med, then small, OR use different colored gravel layers. The caveat here is that over time, the soil WILL wash down into the gravel layers and get "dirty". One way to minimize this is to lay a coffee filter, cut to size, on top of the gravel layer before adding soil.
When you water, WATCH CAREFULLY and make sure that the water that percolates to the bottom rises NO MORE THAN AT or BARELY ABOVE the top of the gravel layer.
Be sure to use a porous soil mix -- it should contain at least 1/4 to 1/3 vermiculite and/or perlite. I prefer ones that contain compost. Because there's no way for you to eliminate excess water, you'll need to be extremely careful about fertilizing. Less is more in this case. Another reason to go with compost or with ORGANIC fertilizers since salts in the chemical ones can build up (They also create a crusty mess along the soil line). Be sure to MOISTEN the soil mix before using it, especially if it contains dry peat or coir. You'll have no way of properly moistening dry soil mix after potting. Luke warm water. Fluff/Mix thoroughly and allow to absorb for 30 min ~ 1 hr. The mix should feel like squeezed out sponge, hold in your hand and the mix should form a ball, THEN CRUMBLE. Looks like pie dough just before you add ice water.
Small plants with short roots will have a hard time in a tall vase because the soil at the top will dry out while the soil in the bottom will remain soggy. I think a vining type of plant usually planted in hanging pots would look lovely in a tall vase. You could get a fairly well started one of those, carefully work all the roots loose, and plant in your vase while holding the plant suspended over the top. Fern or fern-like arching foliage plant might work too. Hanging succulents like Burro's tail might be fun too in a taller vase. While in a shorter container, African Violets and cacti might work (obviously cacti need to be watered less often. AV doesn't like soggy soil either.)
Other plants you might try are those that LIKE wet feet. Try the pond section of the garden center. They will have directions regarding how much wetness these plants prefer -- sometimes, water to just at soil level, sometimes 2" so ABOVE soil level, etc.
*** Pay attention to the ultimate/mature size of the plant *** Get your plants at an independent garden center/greenhouse and ASK "HOW BIG DOES THIS GET?" Also, your plant selection will depend on where you'll put them and how much sun/light exposure they'll get. ASK.
If you're thinking edibles use vases at least 4"~5" diameter and 6" deep soil + 1"~2" gravel, one per vase of salad greens like leaf lettuce/ arugula/spinach, carrots (shorter ones), bush beans, and herbs are likely candidates.
Another thing, over time, you'll find that algae will grow on the inside of the glass. You might have to resort to yearly repotting and scrubbing.
Hmm, that's all I can think of for now. Good luck and have fun!
