This list is far from comprehensive (just off the top of my head), but here goes, a breakdown of general alliance followed by commonly cultivated species of each:
Cattleya alliance:
Cattleya
Laelia
Brassavola
Schomburgkia
Sophronitis
Epidendrum
Encyclia (and related genera)
Dendrobium alliance:
Dendrobium
Bulbophyllum
Cirrhopetalum
Mastigion
Dockrillia
Epigenium
Eria
Cymbidium alliance:
Cymbidium
Cymbidiella
Catasetum/Clowesia
Grammatophyllum
Cycnoches
Chysis
Mormodes
Ansellia
Stanhopea
Gongora
Cirrhaea
Cyrtopodium
Eulophia
Oeceoclades
Pleurothallid alliance:
Pleurothallis
Masdevallia
Dryadella
Dracula
Zootrophion
Vanda alliance:
Phalaenopsis
Doritaenopsis
Vanda
Ascocentrum
Neofinetia
Angraecum
Jumellea
Aeranthes
Aerides
Aerangis
Dendrophylax
Campylocentrum
Arethusinae:
Sobralia
Bletia
Bletilla
Phaius
Arundina
Spathoglottis
Calopogon
Cypripedium alliance:
Cypripedium
Selenipedium
Paphiopedilum
Phragmipedium
Mexipedium
Oncidium alliance:
Brassia
Miltonia
Miltoniopsis
Oncidium
Odontoglossum
Tolumnia
Comparettia
Ionopsis
Notylia
Maxillaria alliance:
Maxillaria
Zygopetalum
Lycaste
Anguloa
Bollea
Huntleya
More miscellaneous (although they do have their own alliances):
Habenaria/Platanthera/Pecteilis
Vanilla
Sacoila
Stenorrhynchos
Ludisia
Anoectochilus
Malaxis
Liparis
Macodes
Pleione
---Prem