Random Order:
Xayah & Rakan, Kindred, Illaoi: 2 skins
Aurelion Sol, Ivern, Kled, Ornn, Camille, Kayn, Zoe, Pyke, Taliyah(<soon to be 2): 1 skin
Vel Koz, Zac, Bard, Rumble, Urgot, Yorick, Lissandra, Aatrox, Tahm, Rek'sai: 3 skins
and then a few with 4 skins Ekko, Xerath, and Zed.
I feel like these are the neglected champs RIOT doesn't feed much artistic talent into. If RIOT is looking into making more skins these are the champs to pay attention to.
Moon Lord Aurelion Sol (Has patches of darkness instead of stars) Houseplant Ivern (Has aloe as hair) Poro Rider Kled (Skarl (Did i spell the name right?) is a poro) Carpenter Ornn (Has wooden tools) Updating Camille (Skin changes colour depending on abilities being used) Star Guardian Kayn (Gets bows in his hair and Rhaast gets a bow on his head) Star Guardian Zoe (Wilder hair) Battlecast Pyke (Has more robotic motions) Star Guardian Taliyah (Has a dress and large bow on her shirt)
Yes, there are alot of champions in that list who clearly need more skins.
The only ones I would exclude here are
They are going to receive their 3. skin with SSG and they are still fairly new. They are served enough for the time being.
These 2 are fortunately already confirmed to get skins in the next months.
These are so damn old already and still just have 3 skins... that's really a shame.
I think 
and are some that need it the most, they're hitting the 2 year marker with no skins.
Pirate Kled would be awesome.
Yasuo has 4 skins ( • ~ • ) too if i remember correctly
