Top 500 Icon
The main reason why someone has this one after hitting Top 500, the highest Overwatch rank in Competitive Mode, so pretty much all the best Overwatch players have this rare icon. We have to note that you can also get this one in the Lucioball event, so it doesn't necessarily mean that every player that has it will dominate – it can even be possessed by a Silver rank player.
Kul Tiras & Zandalar Icons
These two icons were only available if you pre-purchased World of Warcraft's Battle for Azeroth expansion. Since it is both a pre-purchase, and content for another game, not many players will have these icons. And well, not only these are the rarest player icons in Overwatch, but also the best ones, in my opinion. Blizzard just knows how to cross-promote their games, which you can see on some of the rarest Overwatch skins, for example (especially on the Genji skin done as Illidan Stormrage).
All Access Pass Icon
This Tracer silhouette is an icon for the true Overwatch League enthusiasts, and it was only available for players who purchased the All-Access Pass. I have personally never seen this one, have you? The rarity of this one might even make you think that the Overwatch League is dead... It's pretty generic, no fireworks here, but any Tracer main would probably be happy after getting this one in a loot box.
Pink Mercy Icon
This Pink Mercy icon was part of a one-time charity event that awarded an amazing Pink Mercy skin and icon for everyone that donated. Sadly, not everyone is expecting this event to come back, and it's a little pity, not only because of the cosmetics, but also the noble goal of it (fight against breast cancer).
Pachimari Hat Icon
Yeah, it's just Pachimari wearing a hat, you're right. This one was a part of the PachiMarchi Challenge, which would guarantee you this beautiful icon, some of the best Overwatch sprays, Junkrat emote, and an epic Roadhog skin. Sadly, this event never happened again, and even if it will, it probably will be launched with a different set of cosmetics.