Wu-Tang is one of the most popular rap groups of all time. The reason is simple: they're awesome.
GZA:

Real Name:
Gary Grice
Background And Wu-Tang:
GZA starting rapping at a very young age with his cousins RZA and Ol' Dirty Bastard in and around New York City and Staten Island. He was hired by record label early in his career under the moniker The Genius. After slow record sales, GZA created Wu-Tang with his cousins and others, and quickly grew in popularity. His solo album Liquid Swords is considered one of the best solo albums recorded by any single member of the group.
Post Wu-Tang:
GZA kept busy from 2001-2007, when Wu-Tang was on hiatus. He released a follow up to Liquid Swords called Legend of the Liquid Sword that failed to sell as well as his first, but was still critically acclaimed. He even dabbled in acting, and was featured on Wu-Tang's 2007 8 Diagrams.
U-God:

Real Name:
Lamont Hawkins
Background and Wu-Tang:
U-God lived in Staten Island early on in his life where he became friends with Raekwon, Method Man, and Inspectah Deck. He was also close with rapper Cappadonna, an associate of the group. Due to a drug arrest, U-God did not get to perform as significantly on Wu-Tang's first album. He was mostly known as Golden Arms then.
Post Wu-Tang:
Golden Arms/U-God was in a dispute with RZA about the amount of attention that had been paid to his solo record. He claimed that he had not received as much exposure as Method Man and other members of Wu-Tang, and attributed it to poor record sales. In 2005, he released Mr. Xcitement, his second solo record, which failed to sell many records. He is currently working on another album.
Method Man:

Real Name:
Clifford Smith
Background and Wu-Tang:
Method Man grew up in Staten Island, where his young life experiences motivated him to making it in the rap world. He formed Wu-Tang with RZA and was always one of the most famous members. His solo album Tical was the first released by any Wu-Tang members, and was incredibly popular.
Post Wu-Tang:
Method Man started acting in the early 2000's. In 2004 he had a part in Garden State and had a part on HBO's The Wire and CBS' CSI. He was also in How High, but...let's not talk about that.
Meth was a part of some unwanted controversy when radio host Wendy Williams released highly personal information about him and his personal life in 2006. She discussed Method's wife's cancer and even claimed he was having an affair with her doctor.
He was arrested for marijuana posession in 2007, but has continued to make concert appearances and television appearances.
Ghostface Killah:

Real Name:
Dennis Coles
Background and Wu-Tang:
Ghostface met the other Wu-Tang members in Staten Island, where he grew up. He helped form Wu-Tang with RZA and contributed to bringing the other members of the group together. He was featured extensively on Raekwon's albums.
Post Wu-Tang:
Ghost has released 7 solo albums, most recently, The Big Doe Rehab, which was positively reviewed by critics but sold modestly due to internet downloading.
RZA:

Real Name:
Robert F. Diggs
Background and Wu-Tang:
RZA started rapping in the 80s, and upon the creation of Wu-Tang, RZA was regarded the leader. From the beginning, he took control of the group, promising that were he given complete authority, the group would reach the top. The group consented, and RZA delivered. After the release of Wu-Tang Forever, the group was free to pursue any project they liked, and RZA produced most of them himself.
Post Wu-Tang:
RZA has been busy since Wu-Tang ended. He's produced many rap and hip-hop albums, as well as creating music for motion pictures Blade: Trinity and Kill Bill, receiving a Grammy award for his work on the latter. He has also dabbled in acting and directing. He has recently collaborated with The Red Hot Chili Peppers guitarist John Frusciante, former Rage Against The Machine frontman Zach de la Rocha, and Isaac Hayes.
He hasn't slowed down at all since his Wu-Tang days.
Raekwon:

Real Name:
Corey Woods
Background and Wu-Tang:
Raekwon grew up in Brooklyn, and joined Wu-Tang to perform on the debut album Enter The Wu-Tang: 36 Chambers. He is known for his story-telling style of rapping, which enables him to write weaving narratives describing his subjects in detail. His solo album Only Built 4 Cuban Linx... was massively successful upon its debut and is considered by many to be the most influential solo album released by any Wu-Tang member and even one of the most influential rap albums of the 1990s.
Post Wu-Tang:
Raekwon also got into acting when Wu-Tang slowed down, and received a role in the 1999 film Black and White. While filming a documentary about the illegal blood diamond trade in Africa, Raekwon received the distinction of being the first American rap artist to perform in Sierra Leone.
Only Built 4 Cuban Linx II..., a sequel to the original, is set to be released in March 2009.
Inspectah Deck:

Real Name:
Jason Hunter
Background and Wu-Tang:
Inspectah Deck grew up in Staten Island, New York, alongside Wu-Tang members Method Man, Ghostface Killah, and Raekwon. Despite his notability as a fan and critical favorite for his performances on many Wu-Tang cuts, Inspectah Deck has not achieved the same level of solo success as other Wu-Tang members.
Post Wu-Tang:
Inspectah Deck contributed to Only Built 4 Cuban Linx... by Raekwon, Ironman by Ghostface Killah and Liquid Swords by GZA. His only solo projects failed to see much popularity, prompting him to focus on his work with Wu-Tang on their subsequent albums, and on Raekwon's follow up to Only Built 4 Cuban Linx...
Masta Killa:

Real Name:
Elgin Turner
Background and Wu-Tang:
Wu-Tang fans always considered Masta Killa to be the quietest, most mysterious member of the Clan. He was the last of the 9 to join the group, and stuck closely to GZA, who mentored him during his early rapping days with the group. He is noticeably absent from "Protect Ya Neck," Wu-Tang's first single, due to him joining the group after its recording. He is notably quiet during interviews and is the least visible group member. He is known for his flowing rap style.
Post Wu-Tang:
He did not release a solo album, No Said Date, until 2004, well after the rest of the group. It was positively acclaimed by critics and fans alike, who believed the album was most reminiscent of Wu-Tang's early days. He released his second album, Made In Brooklyn in 2006.
Old Dirty Bastard:

Real Name:
Russell Jones
Background and Wu-Tang:
ODB grew up and rapped alongside his cousins RZA and GZA in Brooklyn as youngsters. The trio often traveled into the city to perform and battle other MCs. They were known as All In Together Now Crew. He was known for his on and off-stage antics and unique rapping style and dirty lyrics which helped cement Wu-Tang's unique style. He was not as prominent on Wu-Tang's second release, but contributed a solo track. He released a solo album in 1995 entitled Return To The 36 Chambers: The Dirty Version.
Post Wu-Tang:
He ran into quite a bit of legal trouble after his Wu-Tang days, both with drugs and automobile accidents. His behavior became more erratic, and he even jumped on stage during Shawn Colvin's acceptance speech at the 1998 Grammy Awards. it was not all negative, however. He and friends witnessed an accident and rescued a young girl from the burning wreckage. He visited her in the hospital until she recovered.
Sadly, ODB died on November 13, 2004 after complaining of chest pain due to an accidental overdose of painkillers.