The terms "Rock," "Metal," and "Alternative Rock" are incredibly broad. Here's a guide to some major sub-genres. This list only includes a few larger sub-genres that I can think of at this given time. I'll add others if I find them appropriate.
Celtic Rock/Punk
Years of Popularity: Began in the early 1980's, but it is more popular today
Most Notable Bands: Dropkick Murphys, Flogging Molly, the Pogues
Common Instrumentation: Guitar, Electric Bass, Drums, Banjo, Violin (or Fiddle), Bagpipes, Tin Whistle, Accordian, Mandolin
Samples:
Dropkick Murphys - The State of MassachusetsFlogging Molly - Seven Deadly Sins
Symphonic Rock
Years of Popularity: 70s, 90s, and today
Most Notable Bands: Trans-Siberian Orchestra, Metallica + the San Fransisco Symphony Orchestra, Apocalyptica, London Symphony Orchestra, Royal Philharmonic Orchestra
Common Instrumentation: Orchestral Instruments, Electric Guitar, Electric Bass, Electric Violin
Samples:
Metallica with the San Fransisco Symphony Orchestra - Until it Sleeps
Apocalyptica - Bittersweet
Vanessa Mae - Storm
Industrial
Years of Popularity: 90s - Today
Most Notable Bands: Nine Inch Nails, Rammstein, Depeche Mode and Disturbed are known to venture within the realm of industrial music
Common Instrumentation: Electric Guitar, Electric Bass, Drums, Drum Machine, Synthesizer, Keyboards
Samples:
Rammstein - AmerikaDepeche Mode - Personal Jesus
Grunge
Years of Popularity: 1989-1995 (post-grunge 1995-today)
Most Notable Bands: Pearl Jam, Soundgarden, Nirvana, Screaming Trees, Alice in Chains (post-grunge: Days of the New, Foo Fighters)
Common Instrumentation: Electric Guitar, Electric Bass, Drums
Samples:
Pearl Jam - Even FlowAlice in Chains - No ExcusesDays of the New - Touch, Peel, and Stand

Psychadelic Rock
Years of Popularity: Mid 1960's
Most Notable Bands: The Beatles, Iron Butterfly, Jefferson Airplane, The Jimi Hendrix Experience
Common Instrumentation: Electric Guitar, Electric Bass, Drums, Synthesizer, Organ
Samples:
Iron Butterfly - In-A-Gadda-Da-Vida (In The Garden of Eden) Note: This song is famous for being 17 minutes long.
Jimi Hendrix - Wild Thing
Rockabilly
Years of Popularity: 1950's, 1980s
Most Notable Bands: Elvis Presley, Johnny Cash, Bill Kirchen
Common Instrumentation: Electric Guitar, Guitar, Drums, Keyboards, Double Bass (Upright/Acoustic Bass)
Samples:
Elvis Presley - Jailhouse RockBill Kirchen - Hot Rod Lincoln
Indie Rock
Years of Popularity: 1980's - Today
Most Notable Bands: Radiohead, The Strokes, The Vines, The Rapture, The Killers
Common Instrumentation: Electric Guitar, Guitar, Electric Bass, Keyboards
Samples:
The Killers - BonesThe Rapture - Whoo! Alright, yeah! Uh huh...The Strokes - Reptilia
Arena Rock (often referred to as "Hair Rock," as a reference to the associated hair style of many bands)
Years of Popularity: Late 1970's - 1980's
Most Notable Bands: Boston, Styx, Foreigner, Journey, Queen, Bon Jovi
Common Instrumentation: Electric Guitar, Electric Bass, Drums, Keyboards
Samples:
Boston - More Than A Feeling
Bon Jovi - Livin' On a Prayer
Punk
Years of Popularity: 1970's - 1980's
Most Notable Bands: The Clash, The Ramones, The Sex Pistols
Common Instrumentation: Electric Guitar, Electric Bass, Drums, anything else that makes noise
Samples:
The Clash - London Calling
The Ramones - Rock N' Roll High School
Heavy Metal
Years of Popularity: 1970's - Today
Most Notable Bands: Led Zeppelin, Black Sabbath, Deep Purple
Common Instrumentation: Electric Guitar, Electric Bass, Drums, Keyboards
Samples:
Led Zeppelin - Black DogBlack Sabbath - ParanoidDeep Purple - Hush (Cover)
Ska
Years of Popularity: 1980's - Peak in late 1990's
Most Notable Bands: 311, Sublime, The Mighty Mighty Bosstones
Common Instrumentation: Electric Guitar, Electric Bass, Drums, Saxophone, Trumpet
Samples:
Sublime - SanteriaMighty Mighty Bosstones - The Impression That I Get
Alternative Metal/Nu Metal
Years of Popularity: Late 1980's - Today
Most Notable Bands: Korn, Linkin Park, System of a Down, Coheed and Cambria
Common Instrumentation: Electric Guitar, Electric Bass, Drums
Samples:
Korn - Freak on a LeashSystem of a Down - Chop Suey!
New Wave/Art RockYears of Popularity: 1960's - Today, although stylings have changed through the years
Most Notable Bands: David Bowie, David Byrne, Brian Eno (early); Moby, The Mars Volta (modern)
Common Instrumentation: Keyboards, Synthesizer, Drums, Electric Guitar, Electric Bass
Samples:
The Talking Heads - Burning Down the HouseThe Mars Volta - GoliathMoby - Porcelain