Much of the focus has to do with the characters powers although it should be noted that eyes are said to be the windows to the souls. In RWBY souls are connected to Auras and Semblances so this makes sense.
- Neo- Normally she has one pink and one brown eye though she can change them. They turned white when Raven showed up and green when she was fighting with CME.
- Yang Xiao Long- When she gets mad and her powers amp up they go from purple to red.
- Raven and Qrow Branwen- Their twins that both have red eyes and while neither seem connected to powers it's still worth noting. They have eye symbols with Raven having the right and Qrow having the left. Since there have been clues their based on Odin's birds this might be more meaningful.
- Tyrian- His eyes are usually yellow but changed to purple twice which leads many including myself to believe it means he's using toxin in his stinger. Some questioned whether Tyrian is blind or has poor eye sight based on his fight with Qrow. I don't think he's blind which I'll explain below.
- Fall Maidens/Cinder Fall- Flames appeared around Amber and Cinder's eyes. Interestingly Pyrrha's were shut when she was in the middle of the failed power transfer. Now Cinder is missing an eye thanks to Ruby which Tyrian wanted to repay by taking Ruby's eye in return.
- Ruby Rose- Her silver eyes are the first thing Ozpin mentions upon meeting her and turn out to be important as the silver eyed warriors are known for being the "best of the best." This power is first triggered when Ruby witnesses Pyrrha dying. Hazel dismiss the SEWs as being a threat saying they were dealt with before. Ruby got her eyes from her mother who is presumed dead.
- Salem- The red irises glow but not much is known about her at this point.
Those are all the ones I can think of on top of my head but something did come in mind when thinking about how important eyes seem to be in the series.
- Jaune Arc- When Cardin briefly triggered his Semblance the white light of Jaune's Aura came from his head. It's hard to see what's happening and could simply be because Cardin was aiming for the face which Jaune was unknowingly protecting. But what if the power was coming from his eyes? Jaune doesn't have rare eyes like Ruby as others are seen with blue eyes although his family has been mentioned a few times.
- When Tyrian gets interested in Jaune it's when he's staring at his face (maybe his eyes.) Jaune expression quickly changes from wide eyed surprise to fierce which in turn makes Tyrian take notice. I slowed down the reaction when trying to catch the details and Tyrian's smile widens before he moves in for a closer look. This bit would be meaningless if Tyrian really was blind.