The Chaos Emeralds can be anywhere, usually located in a "Special Stage". Even alone, their power is unmatched by anything else in the entire universe, however, their power can be halted at any time by the Master Emerald. In Sonic the Hedgehog, there were 6 Chaos Emeralds located in 2D rotating Special Stages, and Sonic could not become super with only 6. Sonic 2 was the first game to introduce all 7, in pseudo-3D Special Stages where Sonic & Tails continuously run foward on a path that sometimes curves). In Sonic 3 and Sonic & Knuckles, the 7 emeralds are located in pseudo-3D special stages that rotate entirely when you turn, and you must attempt to collect all the Blue Spheres located in the stage. The Chaos Emeralds appear as plot items in Sonic Adventure and Sonic Adventure 2. In Sonic Adventure, the Chaos Emeralds were collected by Dr. Eggman in order to feed Chaos, a water beast that changed form every time it received a Chaos Emerald. With all 7 it became Perfect Chaos, and used all of the negative energy in the emeralds before dropping them onto the ground. Sonic then picked all 7 up and used the positive energy to become Super Sonic and defeat Perfect Chaos. In Sonic Adventure 2, Sonic and Shadow had the ability to use the Chaos Emeralds to "Chaos Control", alter time and space and teleport or freeze time. Shadow collected the Emeralds for Dr. Eggman to power the ARK, at which point Biolizard took over the station. Biolizard became FinalHazard, and then Sonic and Shadow had to team up and use the Chaos Emeralds (it is believed Sonic used the positive energy and Shadow used the negative energy, but no proof has been given) to become Super and defeat FinalHazard.
Tikal found Chaos and the chao in her ancient Echidna family. She loved them and cared for them, but her father found out about them and wanted the power of the chaos emeralds for himself. He attacked the emeralds and stole them for himself- sealing Chaos away inside the master emerald, killing Tikal in the process. We know this as Tikal's spirit is of the age when she died, which is the age at which her father attacked the emerald. The Chao lived on and bred however.
This is the point at which the Echidnas took over in protecting the emeralds. Knuckles is the Echidna that protects them in the time of the current Sonic the hedgehog timeline, and probably the only Echidna left (In the official storyline, fan comics claim there are other Echidnas).
The most powrerful emerald, the Master Emerald, keeps Knuckles' home (an island paradise called Angel Island) afloat and safe from disaster. It is not known if the island was afloat in the time of Tikal.