Finches belong to the order of Passeniformes (perching birds) and the family of Fringillidae (true-finches). They are seed-eating song birds which explains why they are so common at bird feeders. There are four sub-families, 23 genera, and 994 species (from Wikipedia).
Those subsets shown elsewhere are highlighted in green.
Family Fringillidae
Subfamily Fringillinae – fringilline finches. Three species, which feed their young on insects and few if any seed
Genus Fringilla
Chaffinch Fringilla coelebs
Blue Chaffinch Fringilla teydea
Brambling Fringilla montifringilla
Subfamily Carduelinae – cardueline finches. A much larger group that contains several genera which feed their young mainly on seeds. This subfamily consists of several well-defined clades.
Typical grosbeaks - see Grosbeaks
Bullfinches - see Bullfinches
Genus Pinicola – Pine Grosbeak
Genus Pyrrhula – bullfinches
Arid-zone clade
Genus Leucosticte – mountain finches
Genus N.N. – Dark-breasted Rosefinch, "Carpodacus" nipalensis
Genus Rhodopechys – Trumpeter Finch and relatives
American rosefinches
Genus Carpodacus
Cassin's Finch, Carpodacus cassinii
Purple Finch, Carpodacus purpureus
House Finch, Carpodacus mexicanus
Asian rosefinches
Genus Carpodacus – rosefinches – large number
Genus Haematospiza – Scarlet Finch
Genus Uragus – streaked rosefinches
Goldfinch-canary-crossbill clade (Carduelis and Serinus are polyphyletic and are probably best regarded as a collection of independent sub-groups or genera.)
- Genus Serinus sensu lato – canaries, African seedeaters, serins and African siskins
- (Sub)Genus Serinus sensu stricto – European Serin and relatives (possibly related to Spinus)
- Yellow-fronted Canary Serinus mozambicus
- (Sub)Genus Crithagra – Afrotropical canaries, African seedeaters, citrils (probably only distantly related to Serinus)
- Genus Linurgus – Oriole Finch (possibly basal to Crithagra)
- Genus Rhynchostruthus – golden-winged grosbeaks (tentatively placed here)
- Genus "Serinus" thibetanus – Tibetan Serin (probably related to Spinus and Serinus sensu stricto)
- Genus Carduelis sensu lato
- (Sub)Genus Carduelis sensu stricto – European Goldfinch, Citril Finch and Corsican Finch (probably only distantly related to Spinus)
- (Sub)Genus Spinus – siskins and American goldfinches
- (Sub)Genus Chloris – greenfinches and Desert Finch
- Greenfinch or European Greenfinch Carduelis chloris
Genus Pyrrhoplectes – Gold-naped Finch
Genus Callacanthis – Spectacled Finch
Genus Neospiza – Sao Tomé Grosbeak
Subfamily Drepanidinae – see Hawaiian honeycreepers.
Subfamily Euphoniinae – Euphonious finches - see Weaver Finches.
Genus Euphonia – euphonias
Genus Chlorophonia – chlorophonias
Tanager-finches
- Genus Amaurospiza – blue seedeaters (4 species) - may belong with certain grosbeaks (Cyanocompsa) in the family Cardinalidae.
- Genus Acanthidops – Peg-billed Finch
- Genus Camarhynchus – tree-finches (5–6 species)
- Genus Catamenia – atypical seedeaters (3 species)
- Genus Certhidea – warbler-finches (2 species)
- Genus Charitospiza – Coal-crested Finch
- Genus Coereba – Bananaquit
- Genus Coryphaspiza – Black-masked Finch
- Genus Coryphospingus (2 species)
- Genus Diglossa – typical flowerpiercers (14 species)
- Genus Diglossopis – blue flowerpiercers (4 species)
- Genus Diuca – diuca-finches (2 species)
- Genus Dolospingus – White-naped Seedeater
- Genus Donacospiza – Long-tailed Reed-finch
- Genus Emberizoides – grass-finches (3 species)
- Genus Embernagra (2 species)
- Genus Euneornis – Orangequit
- Genus Geospiza – ground finches (6 species)
- Genus Gubernatrix – Yellow Cardinal
- Genus Haplospiza (2 species)
- Genus Idiopsar – Short-tailed Finch
- Genus Incaspiza (5 species)
- Genus Lophospingus (2 species)
- Black-crested Finch Lophospingus pusillus
- Genus Loxigilla – Antillean bullfinches (4 species)
- Genus Loxipasser – Yellow-shouldered Grassquit
- Genus Melanodera (2 species)
- Genus Melanospiza – St. Lucia Black Finch
- Genus Melopyrrha – Cuban Bullfinch
- Genus Nesospiza – Tristan da Cunha finches (3 species)
- Genus Oryzoborus – seed-finches (6 species)
- Genus Paroaria – cardinal-tanagers (5 species)
- Genus Phrygilus – sierra-finches (11 species)
- Genus Piezorina – Cinereous Finch
- Genus Pinaroloxias – Cocos Island Finch
- Genus Poospiza – warbling-finches (17 species)
- Genus Rhodospingus – Crimson-breasted Finch
- Genus Rowettia – Gough Finch
- Genus Saltatricula – Many-colored Chaco-finch
- Genus Sicalis – yellow-finches (12 species)
- Genus Sporophila – typical seedeaters (some 55 species)
- Genus Tiaris – typical grassquits (5 species)
- Genus Volatinia – Blue-black Grassquit
- Genus Xenospingus – Slender-billed Finch
Family Thraupidae
Genus Geospiza endemic to the Galapagos Islands
Large Cactus Finch (Geospiza conirostris)
Sharp-beaked Ground Finch (Geospiza difficilis)
Vampire Finch (Geospiza difficilis septentrionalis)
Medium Ground Finch (Geospiza fortis)
Small Ground Finch (Geospiza fuliginosa)
Large Ground Finch (Geospiza magnirostris)
Common Cactus Finch (Geospiza scandens)
Genus Diuca
- White-winged Diuca Finch, Diuca speculifera
- Common Diuca Finch, Diuca diuca
Great Inca Finch, Incaspiza pulchra