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Description
Here are the many varieties of filamentous integument that have evolved in Avemetatarsalia. It's more complex than just the five stages!
References
Godefroit, P.; Sinitsa, S.M.; Dhouailly, D.; Bolotsky, Y.L.; Sizov, A.V.; McNamara, M.E.; Benton, M.J.; Spagna, P. (2014). "A Jurassic ornithischian dinosaur from Siberia with both feathers and scales". Science 345(6195): 451-5.
Hone, D.W.E.; Tischlinger, H.; Xu, X.; Zhang, F. (2010). "The Extent of the Preserved Feathers on the Four-Winged Dinosaur Microraptor gui under Ultraviolet Light". PLoS ONE 5(2): e9223.
Kellner, A.W.A.; Wang, X.; Tischlinger, H.; Campos, D.dA.; Hone, D.W.E.; Meng, X. (2010). "The soft tissue of Jeholopterus (Pterosauria, Anurognathidae, Batrachognathinae) and the structure of the pterosaur wing membrane". Proceedings of the Royal Society B, 277(1679).
Lu, J.; Brusatte, S.L. (2015). "A large, short-armed, winged dromaeosaurid (Dinosauria: Theropoda) from the Early Cretaceous of China and its implications for feather evolution". Scientific Reports 5: 11775.
Rauhut, O.W.M.; Foth, C.; Tischlinger, H.; Norell, M.A. (2012). "Exceptionally preserved juvenile megalosauroid theropod dinosaur with filamentous integument from the Late Jurassic of Germany". Proceedings of the National Academy of Sciences, 109(29): 11746-51.
Xu, X.; Wang, K.; Zhang, K.; Ma, Q.; Xing, L.; Sullivan, C.; Hu, D.; Cheng, S.; Wang, S. (2012). "A gigantic feathered dinosaur from the Lower Cretaceous of China". Nature 484: 92-5.
Xu, X.; Zheng, X.; Sullivan, C.; Wang, X.; Xing, L.; Wang, Y.; Zhang, X.; O'Connor, J.K.; Zhang, F.; Pan, Y. (2015). "A bizarre Jurassic maniraptoran theropod with preserved evidence of membranous wings". Nature 521: 70-3.
Xu, X.; Zheng, X.; You, H. (2009). "A new feather type in a nonavian theropod and the early evolution of feathers". Proceedings of the National Academy of Sciences 106(3), 832-4.
Zhang, F.; Zhou, Z.; Xu, X.; Wang, X.; Sullivan, C. (2008). "A bizarre Jurassic maniraptoran from China with elongate ribbon-like feathers". Nature 455: 1105-8.
Zheng, X.; You, H.; Xu, X.; Dong, Z. (2009). "An Early Cretaceous heterodontosaurid dinosaur with filamentous integumentary structures". Nature 458: 333-6.
Quotes denote nicknames I give to filament types that, as far as I know, don't have a widely or technically used name yet. Tan vanes are made of many branching filaments, red vanes are solid.
Update 3/23/17: Added a few things I missed - kudos to 
for pointing them out! Interestingly the feathers of DIP-V-15103 (the amber tail) clearly show an incompletely developed rhachis, seemingly bridging the gap between stages 2 and 3. It also seems barbules potentially evolved before the rhachis!
for pointing them out! Interestingly the feathers of DIP-V-15103 (the amber tail) clearly show an incompletely developed rhachis, seemingly bridging the gap between stages 2 and 3. It also seems barbules potentially evolved before the rhachis!Update 12/17/18: Here's a long-overdue overhaul of this infographic. Added new feather morphotypes present in Liaoning fossils and modern birds, as well as new information on other types in stem-birds. It should be noted that the presence of Classic Stage 2 feathers in anurognathids - which just came out today - has been questioned. David Unwin and Mark Witton both consider it possible these structures, which are only found on the wings, may in fact be degraded actinofibrils (pterosaur wing fibers) and not filamentous integument. Hopefully further studies will be able to tell us the true nature of these structures. Kudos to 
for help regarding feathers in neornithes and enantiornithes. Please let me know if I'm missing anything!
for help regarding feathers in neornithes and enantiornithes. Please let me know if I'm missing anything!Update 3/16/20: Updated a bit of the distributions based on Xu 2020 and an extant bird morphotype I missed. Also renamed, because it covers the bird total group now!
Update 12/22/20: Updated distributions from new information on compsognathids. The broad monofilamentous integument (BMFIs) on Ubirajara (which should be repatriated to Brazil) are similar enough to previously-described EBFFs to be considered the same here.
Update 5/9/22: Updated plumage of Tupandactylus after Cincotta et al. 2022.
Bell, P.R.; Hendrickx, C. (2020). "Epidemeral complexity in the theropod dinosaur Juravenator from the Upper Jurassic of Germany". Palaeontology in press.
Brush, A.H. (1965). "The Structure and Pigmentation of the Feather Tips of the Scaled Cuckoo (Lepidogrammus cumingi)". The Auk 82(2): 155-60.
Brush, A.H. (1965). "The Structure and Pigmentation of the Feather Tips of the Scaled Cuckoo (Lepidogrammus cumingi)". The Auk 82(2): 155-60.
Brush, A.H. (1967). "Additional Observations on the Structure of Unusual Feather Tips". The Wilson Bulletin 79(3): 322-7.
Chen, P.; Dong, Z.; Zhen, S. (1998). "An exceptionally well-preserved theropod dinosaur from the Yixian Formation of China". Nature 391: 147-152.
Cincotta, A.; Nicolai, M.; Campos, H.B.N.; McNamara, M.; D'Alba, L.; Shawkey, M.D.; Kischlat, E.-E.; Yans, J.; Carleer, R.; Escuillie, F.; Godefroit. F. (2022). "Pterosaur melanosomes support signalling functions for early feathers". Nature 604: 684-688.
Currie, P.J.; Chen, P. (2001). "Anatomy of Sinosauropteryx prima from Liaoning, northeastern China". Canadian Journal of Earth Sciences 38(12): 1705-27.Godefroit, P.; Sinitsa, S.M.; Dhouailly, D.; Bolotsky, Y.L.; Sizov, A.V.; McNamara, M.E.; Benton, M.J.; Spagna, P. (2014). "A Jurassic ornithischian dinosaur from Siberia with both feathers and scales". Science 345(6195): 451-5.
Hone, D.W.E.; Tischlinger, H.; Xu, X.; Zhang, F. (2010). "The Extent of the Preserved Feathers on the Four-Winged Dinosaur Microraptor gui under Ultraviolet Light". PLoS ONE 5(2): e9223.
Kellner, A.W.A.; Wang, X.; Tischlinger, H.; Campos, D.dA.; Hone, D.W.E.; Meng, X. (2010). "The soft tissue of Jeholopterus (Pterosauria, Anurognathidae, Batrachognathinae) and the structure of the pterosaur wing membrane". Proceedings of the Royal Society B, 277(1679).
Lu, J.; Brusatte, S.L. (2015). "A large, short-armed, winged dromaeosaurid (Dinosauria: Theropoda) from the Early Cretaceous of China and its implications for feather evolution". Scientific Reports 5: 11775.
Mayr, G.; Pittman, M.; Saitta, E.; Kaye, T.G.; Vinther, J. (2016). "Structure and homology of Psittacosaurus tail bristles". Palaeontology 59(6): 1475-4983.
O'Connor, J.K.; Chiappe, L.M.; Chuong, C.-M.; Bottjer, D.J.; You, H. (2012). "Homology and Potential Cellcular and Molecular Mechanisms for the Development of Unique Feather Morphologies in Early Birds". Geosciences (Basel) 2(3): 157-77.
Pu, H.; Kobayashi, Y.; Lu, J.; Xu, L.; Wu, Y.; Chang, H.; Zhang, J.; Jia, S. (2013). "An Unusual Basal Therizinosaur Dinosaur with an Ornithischian Dental Arrangement from Northeastern China". PLoS ONE 8(5): e63423.Rauhut, O.W.M.; Foth, C.; Tischlinger, H.; Norell, M.A. (2012). "Exceptionally preserved juvenile megalosauroid theropod dinosaur with filamentous integument from the Late Jurassic of Germany". Proceedings of the National Academy of Sciences, 109(29): 11746-51.
Van der Reest, A.J.; Wolfe, A.P.; Currie, P.J. (2016). "A densely feathered ornithomimid (Dinosauria: Theropoda) from the Upper Cretaceous Dinosaur Park Formation, Alberta, Canada". Cretaceous Research 58: 108-117.
Saitta, E.T.; Gelernter, R.; Vinther, J. (2017). "Additional information on the primitive contour and wing feathering of paravian dinosaurs". Palaeontology 61(2).
Smyth, R.S.H.; Martill, D.M.; Frey, E.; Rivera-Sylva, H.E.; Lenz, N. (2020). "A maned theropod dinosaur from Gondwana with elaborate integumentary structures". Cretaceous Research in press.
Wang, M.; O'Connor, J.K.; Pan, Y.; Zhou, Z. (2017). "A bizarre Early Cretaceous enantiornithine bird with unique crural feathers an an ornithuromorph plough-shaped pygostyle". Nature Communications 8: 14141Smyth, R.S.H.; Martill, D.M.; Frey, E.; Rivera-Sylva, H.E.; Lenz, N. (2020). "A maned theropod dinosaur from Gondwana with elaborate integumentary structures". Cretaceous Research in press.
Xing, L.; McKellar, R.C.; Xu, X.; Li, G.; Bai, M.; Persons, W.S.; Miyashita, T.; Benton, M.J.; Zhang, J.; Wolfe, A.P.; Yi, Q.; Tseng, K.; Ran, H.; Currie, P.J. (2016). "A Feathered Dinosaur Tail with Primitive Plumage Trapped in Mid-Cretaceous Amber". Current Biology 26: 1-9.
Xing, L.; Cockx, P.; McKellar, R.C.; O'Connor, J. (2018). "Ornamental feathers in Cretaceous Burmese amber: resolving the enigma of rachis-dominated feather structure". Journal of Palaeogeography 7:13.
Xu X. (2020). "Filamentous Integuments in Nonavialan Theropods and Their Kin: Advances and Future Perspectives for Understanding the Evolution of Feathers". In: Foth, C.; Rauhut, O.W.M. eds. The Evolution of Feathers From Their Origin to the Present. pp. 67-78.
Xu, X.; Norell, M.A.; Kuang, X.; Wang, X.; Zhao, Q.; Jia, C. (2004). "Basal tyrannosauroids from China and evidence for protofeathers in tyrannosauroids". Nature 431: 680-684.Xu, X.; Wang, K.; Zhang, K.; Ma, Q.; Xing, L.; Sullivan, C.; Hu, D.; Cheng, S.; Wang, S. (2012). "A gigantic feathered dinosaur from the Lower Cretaceous of China". Nature 484: 92-5.
Xu, X.; Zheng, X.; Sullivan, C.; Wang, X.; Xing, L.; Wang, Y.; Zhang, X.; O'Connor, J.K.; Zhang, F.; Pan, Y. (2015). "A bizarre Jurassic maniraptoran theropod with preserved evidence of membranous wings". Nature 521: 70-3.
Xu, X.; Zheng, X.; You, H. (2009). "A new feather type in a nonavian theropod and the early evolution of feathers". Proceedings of the National Academy of Sciences 106(3), 832-4.
Xu, X.; Zhou, Z.; Prum, R.O. (2001). "Branched integumental structures in Sinornithosaurus and the origin of feathers". Nature 410, 200-4.
Yang, Z.; Jiang, B.; McNamara, M.E.; Kearns, S.L.; Pittman, M.; Kaye, T.G.; Orr, P.J.; Xu, X.; Benton, M.J. (2019). "Pterosaur integumentary structures with complex feather-like branching". Nature Ecology & Evolution 3: 24-30.
Zhang, F.; Zhou, Z.; Dyke, G. (2006). "Feathers and 'feather-like' integumentary structures in Liaoning birds and dinosaurs". Geological Journal 41: 395-404Zhang, F.; Zhou, Z.; Xu, X.; Wang, X.; Sullivan, C. (2008). "A bizarre Jurassic maniraptoran from China with elongate ribbon-like feathers". Nature 455: 1105-8.
Zheng, X.; You, H.; Xu, X.; Dong, Z. (2009). "An Early Cretaceous heterodontosaurid dinosaur with filamentous integumentary structures". Nature 458: 333-6.
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In the PWDFT, who possesses the feather? It's not very clear, kinda blury. Is it Crurafispennix?