So here's basically how I order the Sonic games. Order of Sonic's games listed, plus evidence that suggests which order they're in, and adding in the ones about Tails, Knuckles, and Shadow, AND adding in my recent discovery Sonic Advance 3 which wasn't on Sonic's page when I first checked it, leads to...

  1. Sonic the Hedgehog - Sonic's first battle with Dr. Robotnik.
  2. Sonic the Hedgehog 2 - Sonic meets Tails. Robotnik builds the Death Egg.
  3. Sonic the Hedgehog 3 - Death Egg arc continues. Knuckles is introduced, tricked by Robotnik into thinking Sonic is the enemy.
  4. Sonic & Knuckles - Considered Part 2 of Sonic 3, Knuckles realizes Robotnik's trick, Sonic destroys the Death Egg. Knuckles faces Egg Robo and Mecha Sonic, and both are destroyed.
  5. Sonic the Hedgehog 4: Episode 1 - Robotnik revisits his past creations, and once Sonic defeats him, introduces Metal Sonic!
  6. Sonic CD - Sonic meets Amy, sends Metal Sonic falling, and saves Little Planet from Robotnik
  7. Sonic the Hedgehog 4: Episode 2 - Robotnik heals Metal Sonic, Sonic and Tails defeat both on the Death Egg mkII
  8. SegaSonic the Hedgehog - Ray and Mighty are introduced
  9. Tails Adventure - His "last adventure with Sonic" being 4 Episode 2, Tails takes vacation and fights one-time villain Grand Battle Kukku 15th
  10. Knuckles' Chaotix - Knuckles's game I'll say is set right after Tails. Espio, Charmy, and Vector are introduced and help Knuckles and Mighty defend Carnival Island from Robotnik and Metal Sonic
  11. Sonic Chaos - Sonic and Tails battle Robotnik again to save South Island
  12. Sonic Triple Trouble - Sonic and Tails battle Robotnik, Metal Sonic, Nack, and Knuckles, tricked by Robotnik again
  13. Sonic Labyrinth - Robotnik puts the Slow Down Boots on Sonic, but he gains five Chaos Emeralds and removes them
  14. Sonic the Fighters - Sonic, Tails, Knuckles, Amy, Espio, Nack (now Fang), and one-time characters Bark and Bean engage in a tournament over eight (fake) Chaos Emeralds to get to the Death Egg 2 and defeat Robotnik and Metal Sonic.
  15. Sonic 3D Blast - Sonic fights Robotnik to save Flickies' Island
  16. Sonic R - Sonic, Tails, Knuckles, Amy, and Robotnik race for Chaos Emeralds. Metal Sonic comes in twice
  17. Sonic Adventure - Robotnik releases Chaos from the Master Emerald and seeks to use him to take over the world. Big is introduced, Gamma has his story but sacrifices himself, and Sonic calls Robotnik "Eggman".
  18. Sonic Adventure 2 - Shadow and Rouge are introduced. Shadow is seemingly killed saving the world. Eggman begins calling himself by his nickname.
  19. Sonic Advance - Sonic, Tails, Knuckles, and Amy fight Eggman
  20. Sonic Advance 2 - Cream is introduced, and she, Sonic, Tails, and Knuckles fight Eggman
  21. Sonic Advance 3 - Sonic, Tails, Knuckles, Amy, and Cream fight against Eggman and Gemerl
  22. Sonic Heroes - Shadow survives and Omega is introduced. Metal Sonic takes the role of main villain disguised as Eggman
  23. Shadow the Hedgehog - Shadow fights the evil Black Doom, who intended him to destroy Earth, but Shadow realizes his true destiny is to save Earth, and kills Black Doom
  24. Sonic Riders - The Babylon Rogues, Jet, Wave, and Storm, are introduced
  25. Sonic Riders: Zero Gravity - Sonic and Jet must stop rampaging robots led by one-time villain SCR-HD and collect Arks of the Cosmos
  26. Sonic Free Riders - A standard Grand Prix racing game, with a surprise appearance by Metal Sonic at the end
  27. Sonic Rush - Blaze and Eggman Nega are introduced
  28. Sonic Rush Adventure - Sonic and Tails enter Blaze's dimension and fight alongside her against one-time villain Captain Whisker, who really works for Eggman and Eggman Nega, who fall out due to Nega's extreme insanity
  29. Sonic the Hedgehog (2006) - Silver is introduced. Sonic falls in love with one-time character Elise, and features one-time villains Iblis and Mephiles the Dark. In the end, Elise erases Iblis and Mephiles, along with the events of the game, from history.
  30. Sonic Rivals - Sonic, Knuckles, Shadow, and Silver - canonically traveling to the past for the first time - compete with each other to battle Eggman Nega
  31. Sonic Rivals 2 - Sonic and Tails, Knuckles and Rouge, Shadow and Metal Sonic, and Silver and Espio, compete as teams of two to fight Eggman Nega and the interdimensional monster, Ifrit. In the end, Ifrit is destroyed and Eggman Nega is trapped in the Ifrit's fiery dimension forever, presumably to die of dehydration.
  32. Sonic Unleashed - Eggman releases one-time villain Dark Gaia, and his robot assistant Orbot is introduced. Sonic meets one-time character Chip and becomes a werehog, fighting Eggman by day and Dark Gaia's minions by night.
  33. Sonic Colors - Sonic battles Eggman to save aliens called Wisps from Eggman's plan for a mind control ray. Sonic defeats Eggman, but doesn't foil his mind control ray - Eggman screws that up! Oh, and Cubot is introduced.
  34. Sonic Generations - Sonic meets his classic self from the past, as does Tails, and they race through different moments in time after Time Eater, who works for Eggman. Eggman is trapped in limbo, and Sonic finally kills Metal Sonic.
  35. Sonic Lost World - Eggman somehow escapes, but when his new servants the Deadly Six betray him, Sonic and Eggman must work together to defeat them.