Who does rouge love?

Answer 1

Her eye for Shadow:

In Sonic Battle she called Shadow 'not bad looking' and 'a prince', in Sonic the Hedgehog 2006 she tries to talk to Shadow into another issue other than a plan to stop Mephiles and also told him that she'll always remain on his side.

But SEGA rejected storyline of Sonic 2006, so Rouge didn't said it.

In Sonic Heroes she currently wants to comfort Shadow about his problems when he escaped from his statis pod.

Shadow doesn't shows any hints of interest in Rouge.

Her eye for Knuckles:

Knuckles in Sonic X they reveal that Knuckles was Rouge's secret crush there, and she flirts with him by teasing him and calling him 'Knucklehead' or 'Knuckie' (as a cutie name), she also says that 'he's cute when he's angry'. In Sonic Chronicles, Rouge admits to Sonic that Knuckles is cute, but she doesn't know if he was the right type for her, and also when Amy said 'Wait..so Shade is 4000 years old?' and Rouge tells Knuckles that 'Your always in to older women, eh Knuckles?'.

Rouge flirted a lot with Knuckles, since he is emotionally unstable to her.

Her eye for Sonic:

In some games Rouge shows interest to Sonic. In Sonic Battle she had some flirtation with Sonic on the beach to get Emerl. In Sonic Chronicles she flirted a lot with Sonic, Amy was very jealous to it. Sonic helped Rouge in her mission. Rouge usually calls Sonic 'handsome' or 'big blue'.

At the same time Sonic never ignores Rouge.

Answer 2

she does gem hunting with dr. egg man and shadow in sonic adventure 2

She is a world class spy that works for G.U.N and is a treasure hunter.