Shadow and Blaze mostly interacted in the Pre-Super Genesis Wave Sonic Universe comics. They first met when Shadow was fighting Metal Sonic and ended up in the Solution Dimension. Shadow almost drowned but was rescued by Blaze and Marine the Raccoon. A more detailed description of this event can be found here.
Shadow and Blaze met again when they were looking for the Solution Emeralds. While they were against each other at first, they eventually teamed up. At one point, Blaze was hurt and Amy ordered Shadow to carry her. In the end, Shadow was the one who convinced Rouge to let Blaze keep the Sol Emerald instead of taking it to G.U.N.
In the games, no notable interactions happened between the two but they met in a few games. In Sonic Generations, the two were among the many characters cheering on while the Sonics fought the Time Eater, and later were both seen attending Sonic's birthday party, although Shadow was not there in the beginning. The two are also playable characters in every game of the Mario & Sonic series, where they can be members of the same team in team sports (except in the 3DS version of London 2012, where each event only has one of 5 specific sets of 4 characters, and the two are in different sets). They also both appear as playable characters in Sonic Forces: Speed Battle and Team Sonic Racing.
Shadow and Blaze have similar personality traits, as both are serious, quiet and rarely spend time in the company of others, although Blaze is friendlier than Shadow.
The two have apparently interacted before in Sonic Generations. If you look closely in the scene before classic Sonic jumps through the portal, you can actually see Shadow next to Silver and Blaze. You can also see them apparently talking.
- shadaze tag on DeviantArt
- shadowxblaze tag on DeviantArt
- shadxblaze tag on DeviantArt
- blazexshadow tag on DeviantArt
- Shadaze-Lovers fanclub on DeviantArt
- Blaze was originally designed to look more similar to Shadow, although the design might have simply been a silhouette.