There are over 30,000 known variable stars, with more being discovered regularly, so a complete list of every single variable is impossible. The following is a list of known variable stars that are well-known, bright, significant, or otherwise interesting.

• R And
• S And (1885 supernova in the Andromeda galaxy)
• U Ant
• θ Aps
• η Aql
• R Aql
• V Aql
• R Aqr
• T Aqr
• U Ara
• R Ari
• U Ari
• ε Aur
• R Aur
• AE Aur
• R Boo
• W Boo
• X Cam
• VZ Cam
• η Car (the volatile supergiant Eta Carinae)
• l Car
• R Car
• S Car
• γ Cas
• R Cas
• S Cas
• W Cas
• R Cen
• S Cen
• T Cen
• V645 Cen (Proxima Centauri)
• δ Cep
• μ Cep
• S Cep
• T Cep
• U Cep
• SS Cep
• AR Cep
• ο Cet (Mira, "the wonderful")
• T Cet
• U Cet
• W Cet
• R Cha
• R CMa
• VY CMa
• FW CMa
• S CMi
• R Cnc
• X Cnc
• T Col
• R Com
• α CrB (Alphecca)
• R CrB
• S CrB
• T CrB
• U CrB
• V CrB
• W CrB
• R Cru
• R Crv
• χ Cyg
• R Cyg
• U Cyg
• W Cyg
• X Cyg
• RT Cyg
• SS Cyg
• SU Cyg
• CH Cyg
• R Del
• U Del
• EU Del
• β Dor
• S Dor (in the Large Magellanic Cloud)
• R Dra
• T Eri
• R For
• η Gem
• ζ Gem
• R Gem
• U Gem
• S Gru
• α Her
• g Her (30 Her)
• u Her (68 Her)
• S Her
• U Her
• X Her
• R Hor
• U Hor
• R Hya
• U Hya
• VW Hya
• BL Lac (originally thought to be a variable star, but later discovered to be a blazar)
• R Leo
• R Lep (Hind's Crimson Star)
• RX Lep
• R LMi
• RU Lup
• β Lyr
• R Lyr
• RR Lyr
• U Mic
• U Mon
• V Mon
• R Nor
• T Nor
• R Oct
• S Oct
• V Oph
• X Oph
• RS Oph
• BF Oph
• α Ori (Betelgeuse)
• U Ori
• W Ori
• VV Ori
• CK Ori
• κ Pav
• S Pav
• β Peg
• R Peg
• X Peg
• β Per (Algol, "The Demon Star")
• φ Per
• ρ Per
• X Per
• ζ Pho
• R Pic
• TX Psc
• L² Pup
• RS Pup
• T Pyx
• S Scl
• RR Sco
• RS Sco
• RT Sco
• R Sct
• R Ser
• S Ser
• U Sge
• WZ Sge
• RR Sgr
• R Sgr
• U Sgr (in M25)
• RT Sgr
• RU Sgr
• RY Sgr
• VX Sgr
• λ Tau
• T Tau
• SU Tau
• R Tri
• R UMa
• T UMa
• U UMa
• Z UMa
• α UMi (Polaris)
• R Vir
• S Vir
• W Vir
• SS Vir
• R Vul
• U Vul
• Z Vul

Sources

David H. Levy, Observing variable stars : a guide for the beginner