Shingen was not born with the name Shingen. His name at birth was Katsuchiyo. When Katsuchiyo was 13, he married his first wife, a girl from the Uesugi clan. She died a year or so later, (however Shingen would go on to have several other wives and mistresses). Later, when he officially came of age (c. 1535), he received permission from the shogun, Ashikaga Yoshiharu, to use haru in his adult name, and thus he became known as Harunobu, using the haru from the shogun along with nobu from his father`s name. It wasn't until 1551, when he also took the monk`s vows, that he took the name Shingen.
In 1560 and 1565, Shingen discovered two internal plots against him. The first was led by a cousin whom Shingen promptly put to death. The second was led by Shingen`s only son at the time, Yoshinobu and Obu Toramasa. Toramasa had previously been Shingen`s guardian and had probably aided Shingen in the rebellion against Nobutora. After Shingen thwarted this rebellion, Toramasa was forced to commit suicide while Yoshinobu was imprisoned at Tokoji Temple; two years later Yoshinobu died, and it is not entirely clear whether he died from illness or from forced suicide. Either way, it left Shingen temporarily heirless.
In the mid 1560s, Shingen focused on internal affairs in his province of Kai, which includes present-day Yamanashi prefecture and parts of Nagano and Shizuoka prefectures. His greatest achievement was the building of a dam on the Fuji River.
Shingen began taking over the Imagawa lands to the south of Kai in 1568 or 69; at first he apparently had an agreement with Ieyasu to split up the lands between them, but he seems to have violated this agreement in his push to eventually defeat Ieyasu. After this takeover was complete, around 1571, Shingen was the most powerful daimyo in eastern Japan, and the only one who was in a position to stop Oda Nobunaga`s push to defeat Ieyasu. In 1570, Shingen made peace with Hojo Ujimasa, a peace that some believe would have virtually ensured victory over Ieyasu. Alas, Shingen died before he could finish what he had started.
Shingen was an interesting ruler because he was among the first lords to do away with corporal punishment for most offenses and also to tax most of his subjects evenly and allow taxes to be paid in either gold or rice. On the other hand, he could be quite brutal and reportedly kept two cauldrons on hand in which he boiled certain criminals alive. Ieyasu later destroyed the cauldrons but integrated many of Shingen`s policies into the policies of the Tokugawa Shogunate.
There is no general agreement on how Shingen died. Some believe he died of a battle wound; others believe he died of an illness (possibly tuberculosis). There is quite a lot of legend surrounding this, particularly because he kept his fading health a secret from his enemies; after his death, his fourth son and heir, Katsuyori, kept Shingen`s death a secret while he went out to finish his father`s battles. Incidentally, Katsuyori was not particularly successful in this regard.
Modern day Yamanashi prefecture and especially the city of Kofu are practically monuments to Shingen. Shingen was legendary for discovering and using hot springs in his province, and many of these today advertise themselves as "Shingen`s hot springs". There are festivals on his birthday (April 14) and the anniversary of his death (May 14) in and around Kofu. There is a shrine to Shingen in Kofu at which you can purchase such items as Takeda Shingen bath salts. Naturally, there are castle ruins, the temple where Yoshinobu was imprisoned, and a big statue as well.
Sources: http://www.samurai-archives.com and Takeda Yoshihito, a descendant of Shingen (and also my ex-boyfriend)