If you're looking for that other Kenshin, you're at the wrong place.

Uesugi Kenshin is one of the most famous Japanese daimyo in the Sengoku Period, reigning in prominence before Oda Nobunaga rose to power. He was a devout Buddhist, praying to Bishamonten most of the time. Combined with his prowess in the battlefield, he's also often regarded as either Bishamonten's Avatar or the God of War himself. A tamer nickname for him would be the 'Dragon of Echigo'.

Perhaps one of the things that made him famous was his rivalry with fellow warlord Takeda Shingen. The two reputedly clashed in the very same battlefield of Kawanakajima five times... with no clear winner. A very famous, oft-re-depicted scene would be an event in the fourth battle where Kenshin managed to sneak into Shingen's camp on his horse, ready to cut down Shingen... until Shingen grabbed a war fan and deflected most of Kenshin's attacks until he retreated. Despite this rivalry, when outside the battlefield, they were known to be friendly with each other and exchanged gifts often, and helped one another out against other warlords. A famous anecdote is that when Shingen's other enemies cut off his food supply routes, Kenshin secretly provided him with salt. Shingen's nickname, the 'Tiger of Kai', made their rivalry Japan's Trope Codifier for Tiger Versus Dragon.

Once Shingen died (reportedly Kenshin wept openly at this and went into mourning for a time), along with another big rival warlord, Hojo Ujiyasu, Kenshin was free to expand his territory and make his march to the capital... and clash with good ol' Oda Nobunaga at Tedorigawa. Kenshin was utterly victorious, wiping out Nobunaga's army. It would seem that Kenshin would be the one to claim rule over the country...

Then he died midway there, and Nobunaga once again seized his opportunity to reach the capital. That Lucky Bastard.

Another wild, popular rumor is that Kenshin was actually a woman, all based on the rumor that he never married and had no children on his own, thus popularizing either androgynous depictions in other media, or flat out giving him a Gender Flip. All his children were adopted, his successor Kagekatsu (who claimed the position after emerging victorious from an infamous power struggle against his younger brother Kagetora) being the son of Kenshin's older sister. Due to clever political maneuvering, the Uesugi clan continued to exist well into the Meiji period.

Tropes associated with him:

Badass: The dude beat Oda Nobunaga.
Bishounen: Some sources describe him as being very beautiful, and many of his fictional depictions follow this.
Cruel and Unusual Death: Rumors has it that he died while defecating on a toilet of that age... which unknown to him, had a ninja/assassin hiding there, who proceeds to shoot a needle to him right on the ass, and killing him.
Friendly Enemy: His and Shingen's respect for each other was legendary.
Red Baron: Either 'Dragon of Echigo' or 'God of War'.
The Rival: With Shingen, also going up to be one of the most popular rivalries in Japanese history.
- Worthy Rival
Tiger Versus Dragon: He's the Dragon, Shingen is the Tiger.
War God: His nickname referenced Bishamonten, the Buddhist god of war.
Warrior Monk
Wholesome Crossdresser: There were rumours he may have been a woman in disguise.

Works referencing him:

The Uesugi is a playable clan in Shogun: Total War series.
Uesugi Kenshin is playable in Samurai Warriors and for once, isn't such a bishonen like most other depictions (heck, he's voiced by Joji Nakata). As usual, his rivalry with Shingen exists and plays part in his series. The 3rd game includes his sister Aya Gozen.
- Kenshin also appears in Kessen III as one of Nobunaga's oppositions, and is a seriously dangerous enemy.
- In Nobunaga's Ambition, Kenshin also is one of the generals available there. One of the titles also offers a What If? story which confirms the rumor that Kenshin is actually a woman, thus gives a female-Kenshin as a character (in addition to male-Kenshin).
Uesugi Kenshin in Sengoku Basara is An Ice Iaijutsu Practitioner with Super Speed, complete with the androgynous appearance and the voice of Romi Paku. And a tendency to make dramatic (elegant) poses, to match with his battle prowess. He's accompanied with an original character, a kunoichi named Kasuga, who is madly in love with him and has a tendency to orgasm whenever he compliments her (and Kenshin does this a lot). And yes, Shingen's there as his rival too.
Sengoku Otome features a Gender Flip Kenshin who is mostly on the minor side of importance.
Another Gender-flipped Kenshin can be found in Sengoku Rance, being a Lady of War per excellence and one of the romanceable characters in the game, and proved so popular that she's often considered one of the best H-Game heroines ever.
Kenshin also appears in the NHK drama named Fuurin Kazan portrayed by Gackt. Yes. That Gackt.
In Mirage of Blaze he became the actual Bishamonten after his death and established the Underworld Uesugi Army made up of reincarnating spirits of his once-retainers, to protect Japan from vengeful spirits of other Sengoku era generals. The commander of this army is Uesugi Kagetora, one of Kenshin's adopted sons who, in the Sengoku period, was defeated by his older brother Uesugi Kagekatsu in the civil war that erupted over succession of the clan after Kenshin's death, and consequently committed suicide.