Emo

Emo is a genre derived from punk/hardcore. It is well defined and has quite a devoted following on /mu/. If this is your idea of emo, you're sorely wrong. The actual artists and fans of emo look more like this and this.

Some well known entry-level emo bands include: The artists one will find most often in any emo sharethread (and the best place to start) include:
 * Brand New
 * Taking Back Sunday
 * Jawbreaker
 * Rites of Spring
 * Sunny Day Real Estate
 * American Football
 * Cap'n Jazz
 * Snowing
 * Dads
 * Algernon Cadwallader

Emo Origins
Emo originally started in the '80s when Ian MacKaye of Minor Thread decided to make punk music less about politics and hostility; and more about the feelings of the listener. Towards the late 80s and early 90s, "emo-core" bands such as Rites of Spring started popping up. They took very much from hardcore and share little with most modern "twinkly" or "Midwestern" emo. In the mid to late 90s, bands such as Weezer and Jimmy Eat World began to implement more accessible alternative rock vibes to the music, bringing it to a wider audience.

Types of Emo
Twinkly Emo

Emo music characterized by "twinkly" sounding guitars achieved by the use of many hammer-ons and pull-offs.

Math Emo Needs info...

Midwestern Emo
Needs Info...

Screamo
An extreme form of emo characterized by screamed and harsh vocals with typically chaotic and loud sonic qualities. Very upbeat and aggressive instrumentally. Lyrics are similar to standard emo and can range from downtrodden and depressing to angry and dread-filled.

Mainstream Emo
No, bands like My Chemical Romance, Panic! At The Disco, and Alexisonfire aren't emo. They're generic pop punk that scene kids latched onto.
 * Brand New
 * Taking Back Sunday
 * Jimmy Eat World
 * 30 Seconds To Mars
 * Dashboard Confessional

Essential Emo/Screamo Bands
Snowing A combination of math, twinkly, and midwestern emo with shouted vocals. Snowing has gained a massive cult following in the emo community. Probably the best thing about Snowing is that they released all their music for free. Their demo tape "Fuck Your Emotional Bullshit" is only 5 songs. They released an LP entitled I Could Do Anything I Wanted If I Wanted. Snowing broke up in 2011 and played their final show in a church.