From Sonic Retro
Sonic 1 and Sonic CD
Sonic 3 & Knuckles
The giant Ring reappears in Sonic 3 & Knuckles. It transports the player to a Blue Sphere Special Stage. If the player is in the S&K zones of Sonic 3 & Knuckles and has collected all of the Chaos Emeralds, it becomes a flashing Ring that will transport him to the Hidden Palace Emerald Shrine, where he can select which Super Emerald to try to collect. If the player has already collected all the Chaos Emeralds (or Super Emeralds) in the game, the giant Ring will give him 50 Rings when collected.
Sonic 3D Blast
In Sonic 3D Blast, there are Giant Rings over transport tubes and the goal. You need to throw all the Flickies in the area into the ring to warp them to their dimension. Once done, the ring will disappear and the path will open.
The Sonic Blast giant Rings, although almost as small as regular Rings, but thicker, have the same function as those in S3&K. Unlike S3&K, where Special Stages alternate by the order you enter, you will always get the same special stage from the same zone. Also unlike S3&K, there's only one giant Ring per level.
Not a transport feature, these oversized rings appear inside the first special stage and are worth 10 standard Rings each. A similar item crops up in the night levels of Sonic Unleashed, where larger, thicker rings are worth 10.
In Knuckles' Chaotix, not only are there Giant Rings at the end of an act which appear with 50 Rings and will take you to the Special Stage, there are also Giant Rings scattered around the level which will transport the player to the game's Bonus Stage.
Sonic the Hedgehog 4 takes cue from Sonic 1 and Sonic CD. Giant Rings appear at the end of every Zone's first three Acts, allowing access to the Special Stage provided Sonic has at least 50 rings in hand. Unlike previous games however, when all the Chaos Emeralds are collected, they won't appear after collecting 50 rings, as they can be accessed from the Level Select screen.
3D Sonic Games