Rouge the Bat is a world famous treasure hunter. Her voluptuous and daring attitude turns any man's head. Her policy though is that duty comes first, but she has big interest in jewels. Her figure, speech and behaviour masks her true identity. Rouge has a crush on Knuckles the Echidna, but refuses to admit it. Rouge the Bat is very secretive about everything, and very little has actually ever been disclosed about her. She would often switch sides with either the Good or Bad to confuse them.
Rouge the Bat does have allies, such as Shadow the Hedgehog and Topaz from G.U.N. It wasn't until after a few episodes that Rouge and Topaz actually became close friends. At the end of the season in which Topaz and Rouge met, Rouge and the others were transported home. While Rouge said goodbye to Topaz, Topaz had a tear in her eye, remembering all the good times they had. In Season 2, she is one of G.U.N.'s top agents.
She battled against the Metarex in Season 3 with Eggman and released Shadow. She declared war on Eggman after Chris was sent to Earth.
Shadow the Hedgehog
When Rouge first established the business transactions for helping Dr. Eggman and Shadow the Hedgehog find the Chaos Emeralds, she seemed oddly interested in Shadow and showed a fair amount of remorse in the final episode of the series, when staring at the empty caspule she'd found him in. Eggman actually notices this moment and says, "I can't believe it! You're worried about Shadow aren't you?". Rouge denies this, but after asking Eggman where he thinks Shadow might be, she suspects that he knows something that he's not telling her.
Knuckles the Echidna
The two are still rivals like in the games. But the two have a few romantic conversations with each other which hinted their love in a few episodes. The 4Kids website mentions her crush on Knuckles.
Rouge teasing Knuckles.
They appear to hold some sort of rivalry and compete fiercely against each other in the Battle Tournament. Rouge the Bat also attempt to tease Amy in a few scenes as well.
Rouge and Amy in their battle.
She enjoys teasing him, and in the tournament arc of Sonic X she defeats him in battle by kissing him on the cheek.
Rouge manipulating Tails.
Topaz is Rouge's partner. Though at first the regimental Topaz disapproves of the scheming Rouge, (who keeps calling her an old lady), the two become friends fast. Their main assignments involved striking at Eggman and locating the Chaos Emeralds as well as serving as envoys between Sonic and the government. Topaz said farewell to Rouge when she had to return to her planet, Rouge gave her a ring as a goodbye gift. This is quite unusual, as Rouge usually keeps any piece of jewelry she comes across. After Topaz sees Rouge step through the portal back to her home planet, Topaz has an out of character moment where she bursts into tears crying, as opposed to her usual tough and serious nature, suggesting there was a strong friendship between the two. In one episode, however, while Topaz was relaxing on the beach, she called Rouge who said to her that she'd prefer a cave as a vacation spot because she's a bat, and Topaz then understands why Rouge has such a dull social life.
* In Sonic X, Rouge regularly uses the move, "Screw Kick", which allows her to spin like a top while kicking, like that from Sonic Adventure 2. In the 4kids dub, she says "Screw Kick" in Episode 44, like in the Japanese version, but in other episodes she merely just yells or grunts.
* Rouge's theme song, Mysterious and Sexy Thief Rouge was first heard in Episode 11.
There is the basic information on Rouge the Bat from Sonic X. Here you may feel free to discuss about Rouge's character from the show.