I have experimented with onions, celery, and carrots.
We had had some discussions of this before so I tried to find the
thread for the pictures. I just have not found the right search term.
With carrots, the carrot tops make a lovely plant though I have heard that they will not make carrots. Even though they say you can't regrow carrots, in that thread that I was trying to find someone did get it to grow a little carrot if I remember correctly.
Celery and onion are rather successful.
If you are doing your experiment indoors you will need to change your
water every day as it got really slimy for me if I did not change the water every day. I am on well water so that might make a difference.
When I tried it outdoors, some animals got my experiment. I guess it was because they don't have
roots to hold them in the soil.
These were fun experiments.