Hi, Greene! Unfortunately I'm not on the site much these days, but was killing time doing a bit of browsing, ran across this thread, and wanted to comment.
Savannah, think about flower arrangements. Those with greenery in with the flowers. These test tubes are essentially small vases. Many plant cuttings will live weeks, even months in just clean water, even if they don't grow roots.
A couple points to keep in mind. Those cuttings that root will tend to use water fairly quickly, especially considering the small amount of water in a test tube, so you will need to watch that those tubes don't dry out.
Cuttings that don't root may not use water so quickly, but you'll need to watch that the water stays clean. Regular water changes, maybe combined with a bit of a trim of the stem end, will keep these cuttings looking healthy. Sometimes, even these cuttings may eventually develop roots.
Another point to think about when taking cuttings is that plants that do well in shade or partial shade will likely do better long term than plants that require full sun. But don't be afraid to experiment. Gardening is an adventure. Things that should work sometimes don't, and things that shouldn't sometimes do.
Most land plant seed, even if they sprout, would quickly die and rot if left fully aquatic. There are aquatic/bog plants whose seed would sprout and possibly grow in plain water, but even these would likely need a substrate for their roots. Additionally, seed are unlikely to be available commercially.
But cuttings are a quick and easy way to have a desk-top display. As I mentioned before, experiment! If you stick with it you will eventually develop favorites, those that last a reasonable length of time and that give you a look you enjoy.
Good luck, and have fun with your project!
Ron