The number of petals a flower has can be an important key to identifying the flower. Newcombe's Wildflower Guide is based on this concept.
An important thing to remember about this concept is that the "number of petals" represents the number of apparent petals. This is not necessarily the botanically-correct number of petals. Oftentimes what appear to be petals are actually sepals or bracts. It is an aid to identification, not a botanical classification.

Alyssum, Hoary (Berteroa incana)
Bedstraw, Labrador (Galium labradoricum)
Bedstraw, Purple (Galium latifolium)
Bedstraw, Sweet-scented (Galium triflorum)
Bedstraw, Yellow (Galium verum)
Bluehearts (Buchnera americana)
Bower, Virgin's (Clematis virginiana)
Bunchberry (Cornus canadensis)
Celandine (Chelidonium majus)
Clammyweed (Polanisia dodecandra)
Columbo, American (Frasera caroliniensis)
Cranberry, Large (Vaccinium macrocarpon)
Cranberry, Small (Vaccinium oxycoccos)
Cress, Hairy Bitter (Cardamine hirsuta)
Cress, Hairy Rock (Arabis hirsuta)
Cress, Lyre-leaved Rock (Arabidopsis lyrata)
Cress, Purple (Cardamine douglassii)
Cress, Smooth Rock (Borodinia laevigata)
Cress, Spring (Cardamine bulbosa)
Cuckooflower (Cardamine pratensis)
Culver's Root (Veronicastrum virginicum)
Gentian, Narrow-leaved (Gentiana linearis)
Gentian, Smaller Fringed (Gentianopsis virgata)
Gentian, Spurred (Halenia deflexa)
Jumpseed (Persicaria virginiana)
Meadow Beauty (Rhexia virginica)
Meadow Rue, Early (Thalictrum dioicum)
Mustard, Garlic (Alliaria petiolata)
Partridgeberry (Mitchella repens)
Poppy, Celandine (Stylophorum diphyllum)
River Beauty (Chamerion latifolium)
Rocket, Dame's (Hesperis matronalis)
Rocket, Yellow (Barbarea vulgaris)
Saxifrage, Golden (Chrysosplenium americanum)
Shepherd's Purse (Capsella bursa-pastoris)
Snowberry, Creeping (Gaultheria hispidula)
Teasel (Dipsacus fullonum)
Whitlow Grass, Spring (Draba verna)
Woodruff, Sweet (Galium odoratum)

Irregular 2 petals 3 petals 4 petals 5 petals 6 petals 7 or more Indistinguishable

THUMBNAILS
Alyssum, Hoary (Berteroa incana)	Bedstraw, Labrador (Galium labradoricum)	Bedstraw, Purple (Galium latifolium)	Bedstraw, Sweet-scented (Galium triflorum)

Bedstraw, Yellow (Galium verum)	Bluehearts (Buchnera americana)	Celandine (Chelidonium majus)	Clammyweed (Polanisia dodecandra)

Columbo, American (Frasera caroliniensis)	Cress, Hairy Bitter (Cardamine hirsuta)	Cress, Hairy Rock (Arabis hirsuta)	Cress, Lyre-leaved Rock (Arabidopsis lyrata)

Cress, Purple (Cardamine douglassii)	Cress, Smooth Rock (Borodinia laevigata)	Cress, Spring (Cardamine bulbosa)	Cuckooflower (Cardamine pratensis)

Jumpseed (Persicaria virginiana)	Meadow Beauty (Rhexia virginica)	Meadow Rue, Early (Thalictrum dioicum)	Mustard, Garlic (Alliaria petiolata)

Partridgeberry (Mitchella repens)	Poppy, Celandine (Stylophorum diphyllum)	River Beauty (Chamerion latifolium)	Rocket, Yellow (Barbarea vulgaris)

Saxifrage, Golden (Chrysosplenium americanum)	Shepherd's Purse (Capsella bursa-pastoris)	Snowberry, Creeping (Gaultheria hispidula)	Teasel (Dipsacus fullonum)

Whitlow Grass, Spring (Draba verna)	Woodruff, Sweet (Galium odoratum)

Irregular 2 petals 3 petals 4 petals 5 petals 6 petals 7 or more Indistinguishable

To see all Species with 4 Flower Parts in order by Common Name → START HERE