I am on the lookout for natural products (e.g. herbs, spices) that could make interesting chemistry experiments.
There are various places on the web that sell a variety of herbal things and I figure some should have interesting chemistry.

Examples:
Spearmint has (R)-(-)-carvone, while caraway seed has (S)-(+)-carvone, these mirror images smell different to most people.
Red cabbage is a pH indicator.
Turmeric/curcumin is also.
Tea contains caffeine.  (I am working on extract it now...)

Any other suggestions?

I am getting a headache trying to search this forum for a past post on extracts of herbs. That link would have a discussion about the poisonous effects of herb and spice concentration. Someone else fine the link and post it.

How about steam-distilling spices/herbs and then doing separation of the compunds in the essential oil?

Fennel
Anise
Basil
Thyme
Nutmeg
Black pepper
Estragon
Rosemary
Lavendel
Cardamom
Dill
Parsley
Coriander

I could tell you loads more, but these are common and easy to get and work with. Some glassware and a vacuum source is a big plus...

At pharmacies around here you can get a mix of essential oils to make your own "glögg", which is  a kind of spiced wine you drink warm at christmas time.

What's the solvent of choice for chemically extracting extracts from natural things? Denatured alcohol or acetone? (I could make chloroform...but, pass!)

I and probably most people here don't have a lab full of exotic solvents. I do have a bathroom and garage chemicals.

What's the solvent of choice for chemically extracting extracts from natural things?

I think that steam distillation is ideal, but I don't have the glassware now.

Alcohol (190 proof stuff sold as "Everclear") is my first choice solvent, less toxic than alternatives.

I think that steam distillation is ideal, but I don't have the glassware now.

Yes, steam distillation can be pretty ideal. I highly recommend you get some glassware and equipment for that if you already have space for a lab. It's more fun too.

Just remember that essential oils and natural extracts are far from often suitable for consumption. Sometimes they are pretty toxic. I guess you already knew that, I just want to remind you and anyone who reads the thread about it.

I don't suppose Mark wants to get arrested

Texas does have stupid glassware laws.  If I ever speak of a 'flask', that is a hypothetical comment.  I really would mean a beaker that is shaped like a flask.