The following Little Astronomy Blog post comprehensively lists every brightest star for each of the 88 constellations! Each star's name is listed in parentheses next to its respective constellation, followed by the apparent magnitude — visibility to the human eye. Values come from WolframAlpha.
Andromeda — Alpheratz (2.07)
Antlia — α Antliae (4.28)
Apus — α Apodis (3.83)
Aquarius — Sadalsuud (2.87)
Aquila — Altair (0.76-0.77)
Ara — α Arae (2.84)
Aries — Hamal (2.01)
Auriga — Capella (0.08)
Boötes — Arcturus (-0.05)
Caelum — α Caeli (4.44)
Camelopardalis — β Camelopardalis (4.03)
Cancer — Al Tarf (Tarf) (3.53)
Canes Venatici — Cor Caroli (Asterion) (2.89)
Canis Major — Sirius, brightest star in the night sky (-1.44, -1.46)
Canis Minor — Procyon (0.4)
Capricornus — Deneb Algiedi (2.85)
Carina — Canopus, 2nd-brightest star in the night sky (-0.62 to -0.74)
Cassiopeia — usually Schedar (Shedir) (2.24)
...but sometimes Tsih (up to 1.6 and a minimum of 3.0)
Centaurus — α Centauri (Rigel Kent), 3rd-brightest star in the night sky (-0.01)
Cepheus — Alderamin (2.45)
Cetus — Deneb Kaitos ("whale's tail") (2.02-2.04)
Chamaeleon — α Chamaeleontis (4.05)
Circinus — α Circini (3.18-3.21)
Columba — Phact (2.65)
Coma Berenices — β Comae Berenices (4.23)
Corona Australis — Alphekka Meridiana & β Coronae Australis (both about 4.1)
Corona Borealis — Alphekka (Alphecca) (2.21-2.32)
Corvus — Gienah (2.58)
Crater — δ Crateris (3.56)
Crux — Acrux (0.77)
Cygnus — Deneb (1.21-1.29)
Delphinus — Rotanev (3.6)
Dorado — α Doradus (3.3)
Draco — Etamin (2.24)
Equuleus — Kitalpha (3.92)
Eridanus — Achernar (0.45)
Fornax — α Fornacis (3.8)
Gemini — Pollux (1.14, 1.16)
Grus — Alnair (1.73-1.74)
Hercules — Kornephoros (2.78)
Horologium — α Horologii (3.85)
Hydra — Alphard (1.99)
Hydrus — β Hydri (2.82)
Indus — α Indi (3.11)
Lacerta — α Lacertae (2.76-2.777)
Leo — Regulus (1.36)
Leo Minor — Praecipua (46 Leonis Minoris, HIP 53229) (3.79-3.83)
Lepus — Arneb (2.58)
Libra — Zubeneshamali (2.61)
Lupus — α Lupi (2.3)
Lynx — α Lyncis (3.14)
Lyra — Vega (0.03)
Mensa — α Mensae (5.08)
Microscopium — γ Microscopii (4.67)
Monoceros — β Monocerotis (3.76)
Musca — α Muscae (2.68-2.73)
Norma — γ2 Normae (4.01)
Octans — ν Octantis (3.73-3.76)
Ophiuchus — Rasalhague (2.08)
Orion — Rigel (0.18)
Pavo — Peacock (α Pavonis) (1.94)
Pegasus — Enif (usually 2.38, but varies from 0.7 to 3.5)
Perseus — Mirphak (1.79)
Phoenix — Ankaa (2.4)
Pictor — α Pictoris (3.24-3.3)
Pisces — η Piscium (3.62)
Piscis Austrinus — Fomalhaut (1.15-1.17)
Puppis — Naos (2.21-2.25)
Pyxis — α Pyxidis (3.68)
Reticulum — α Reticulii (3.33)
Sagitta — γ Sagittae (3.51)
Sagittarius — Kaus Australis (1.79-1.85)
Scorpius — Antares (0.88-1.16)
Sculptor — α Sculptoris (4.3)
Scutum — α Scuti (3.85)
Serpens — Unukalhai (2.62-2.63)
Sextans — α Sextantis (4.48)
Taurus — Aldebaran (0.87)
Telescopium — α Telescopii (3.49)
Triangulum — β Trianguli (3.0)
Triangulum Australe — Atria (1.91)
Tucana — α Tucanae (2.87)
Ursa Major — Alioth (1.76-1.78)
Ursa Minor — Polaris ("North Star") (1.97)
Vela — Regor (1.74)
Virgo — Spica (0.95-1.1)
Volans — β Volantis (3.77)
Vulpecula — α Vulpeculae (4.44)
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