Many umbelliferous plants are used as vegetables, herbs, and spices. Here’s a list.
But first, a note on terminology: although everyone refers to the spices as “seeds”, they’re actually fruit, specifically a type called schizocarp, a dry fruit that will split into segments, each of which contains one seed; plants in the Apiaceae always have schizocarps that split in two parts. In the text below I’m sticking with common usage and referring to them as seeds. But really they’re fruit.

Daucus carota Although the carrot is a biennial plant, the roots are harvested during the first year of growth. The plant is native to Eurasia, but found in the wild in all the lower 48 states and much of Canada; as wildflowers, they’re called Queen Anne’s lace, and on noxious weed lists in Iowa, Michigan, Ohio, and Washington. Older sources sometimes refer to two subspecies, D. carota ssp. sativus and D. carota ssp. carota; these names are now considered obsolete by ITIS.

Pastinaca sativa Like the carrot, the parsnip is a biennial plant whose roots are harvested during the first year. Also native to Eurasia and now established in North America except in the Deep South. Parsnip is a prohibited noxious weed in Ohio.
Apium graveolens The stalks, leaves, and seeds of celery are used. The plant is a biennial native to central and southern Europe, southwestern Asia and North Africa. Probably. Celery has been cultivated for so long there’s a lot of confusion about its origins. It’s become established in parts of the US, in an arc running from New York south, west, and then north into Washington. The variety A. graveolens var. rapaceum is grown for the root, called celeriac.
Perideridia There are 13 species in this genus, all with the common name yampah. It’s a perennial plant native to western North America. The roots were an important food source for Native Americans.
Arracacia xanthorrhiza Arracacha is a perennial native to the Andes, grown for the edible root.
Foeniculum vulgare Sometimes incorrectly labeled anise, fennel is a perennial grown for the swollen stalks at the base of the plant (the “bulb”). It’s native to the Mediterranean but has naturalized in much of Europe and in the warmer parts of the US. Fennel is on the California Invasive Plant Council’s Invasive Plant Inventory for moderate invasiveness and severe impact (2006 version).
Levisticum officinale The native range of lovage is uncertain; probably Europe or Asia. It’s a perennial and once established can be hard to get rid of. Both the stalks and leaves can be eaten. The flavor is intense, like some sort of super-celery. A little goes a long, long way.
Anthriscus cerefolium (sometimes spelled cereifolium) This southern European native is an annual plant that deserves more respect. Chervil is used mostly in French cuisine, in delicate dishes because the flavor is mild. Although the leaves are sold in dried form, don’t bother buying them; the volatile oils are lost during drying and the result is flavorless. Chervil is trivially easy to grow from seed.
Petroselinum crispum Parsley is a biennial generally used as an annual, since the leaves can get harsh or bitter in their second season. There are scattered populations established in parts of the US, but it’s not listed anywhere as a weed. It’s native range is uncertain, possibly the Levant or nearby areas.
Anethum graveolens Dill is annual, naturalized in much of the US and Canada but native to Asia minor and the Mediterranean. Both leaves and seeds are used. The common name “dill weed” is a clue that this plant is really easy to grow.
Carum carvi Caraway is an established alien in Canada and the northern half of the US (more or less), and a B-list noxious weed in Colorado. It’s a biennial native to Eurasia and north Africa. Caraway seed is familiar as the dominant flavor in rye bread and aquavit.
Pimpinella anisum I blame Alton Brown (of Good Eats fame) for the increasingly widespread mispronunciation of the word “anise”. It’s pronounced ANis, not anEECE (google it). The plant is an annual native to southeastern Europe and southwestern Asia. My Italian forebears would roll in their graves if I used anything other than anise seed to flavor pizzelles.
Myrrhis odorata Both the leaves and seeds of cicely are used as a flavoring, though the use is not widespread. The plant is a perennial native to south-central Europe, with scattered naturalized populations in the US and Canada.
Coriandrum sativum Called cilantro for the leaves, shoots, and roots, and coriander for the seed, this annual is native to southeastern Europe, southwestern Asia, and north Africa. It’s present in parts of North America but not listed as a weed by any authorities.
Eryngium foetidum Grown for the leaves, culantro (often confused with cilantro) is used in Southeast Asia, the Caribbean, and Central America. It also grows in Georgia and Florida. I can’t find any authoritative information about its native range, but it is a tropical annual.
Cuminum cyminum Cumin is an annual plant native to the eastern Mediterranean and central Asia. The seeds are used in many cuisines around the world.
Bunium bulbocastanum The seeds of this perennial plant are known as black cumin, black caraway, and kala jeera. It’s native to southeastern Europe and south Asia.
Trachyspermum ammi Ajwain is an annual native to south Asia, grown for the seeds.
Ferula assa-foetida The dried and ground sap or resin of the roots of this perennial is called asafoetida. The powder is used sparingly in various Indian cuisines, more as a flavor enhancer than a flavor in itself. The plant is native to western Asia.

now my kitchen smells like an Indian restaurant
Many umbelliferous plants contain poisons of various sorts, including some of the plants described above. More on that next time.