This topic is interesting, I like to organize and make best lists of things as well, so this should be fun to compile. I am only doing Sonic Heroes so far as that is the game I have the most experience in, and it will take me a bit more time to find records for other games that I think would be worthy of a list like this. I didn't find a whole lot of records, but I have listed the ones I think deserve to be on such a list. These records are just numbered for organization, they are not in any specific order or rank. Let's dive into it.
Sonic HeroesTimes1.
Hang Castle, Team Rose - 0:38.28 by Sonicspeedruner - This stage is so short yet very difficult to get right. The door clip is annoying and various parts of the stage are tough to pull off correctly. I have spent a lot of time in the past on my 0:43.64 and am I bit hesitant to try to improve it due to the length of time it would take to possibly improve. This is a great time.
Extra1.
Grand Metropolis, Team Rose - 1:24.34 by ShadowJacky - This is a tough one to get right. There are a lot of stops and quick jumps to make that can slow you down a lot, as Team Rose is slower than the other teams. It just is a technically difficult level, one that I have had trouble pulling off a good time successfully. Current record by more than 5 years, and he says it can go below 1:20.00 as well. :O
Rings1.
Ocean Palace, Team Rose - 432 Rings by chainchumper - This is the max it seems for this stage, and he is the first and only person in 1st place so far. You have to do the power formation flight glitch to be able to make it behind the start to get rings there, and then use the thundershoot gauge trick to make it past the goal ring. That is difficult as the camera does not cooperate with you during the big expedition over the ocean past the goal ring, and making it over to the other side of the stage takes time, patience, and effort. An overall test of skill, and a good record to try to get if you want to show off your ring attacking prowess.
2.
Grand Metropolis, Team Sonic (Extra) - 499 Rings by 5 players - I have tried this 5 minute timed ring attack before and it gets really close to the time limit. It is a tough one to do as you have to go a lot of places around the stage to get rings, and by the nature of the stage you just don't have that much time to get the old max of 499. This level is just a flat out tough one, and you need to have skill to get 499 rings within the time limit. I'm sure all 5 players who have this record can attest to that.
3.
Rail Canyon, Team Dark - 539 Rings by Pokemonmaster888 and OmegaDJ - This ring attack is a hard one that requires an imagination and thinking for the 539 rings to be gotten. The first set of trick rings is the hardest, while the other ones are not as difficult. I'm not going into detail here about the strategies; you can refer to my guide I wrote about it years ago:
http://www.soniccenter.org/guides/sonic_heroes/guide289 I personally thought it wasn't too difficult, but as the test of time has shown (and also the fact my guide is out there), only two players have this score after almost 7 years. I encourage you guys to try it and see what you can do with this level. Maybe a lot of people haven't seen my guide; I just know that if you take the time to analyze this level and think of the possible moves you can do, you might be able to pull off this score.
Bosses1.
Egg Hawk, Team Sonic - 0:16.36 by Sonicspeedruner - This boss is a quick one, the strategy to get it done though is a bit tricky. You have to either button mash very fast to get the fire dunks to go quick enough to defeat him, or you have to time the button presses to get them done quick enough. For some reason on my controller/game the more I restart the level, the slower the fire dunks become. Sometimes the fire dunks don't hit the cockpit either, which seems to be random. It's just an awesome time that beat bertin's record of 0:17.11 by close to a full second.
2.
Egg Emperor, Team Sonic - 0:15.98 by Sonicspeedruner - This is his video:
https://www.youtube.com/watch?v=caED9mx6bts The Egg Emperor strategies have been improved numerous times in the past, and now the first Egg Emperor time to be under 16 seconds has a sick strategy. You don't even have to leave the first platform anymore! This is just a solid time, especially due to the fact that getting your teammates to stick to the Egg Emperor's weak spot is a bit difficult. I have been going back and forth with Sonicspeedruner for all of the Egg Emperor times, and with this new strategy, I look forward to keep battling with him for the Egg Emperor bosses. This is a flat out impressive time.
Well, that's all for this list. I'll post sometime in the future when I research more games/stats that could be on my next list. I'll try to research games I am not familiar with as well to include more stats that could be informative to other people.