Chrome is the only browser to have any support for the new Web Components features; it has implemented the Shadow DOM (with the vendor-prefixed webkitShadowRoot() constructor) and templates. Both must be explicitly enabled. Work on custom elements is underway.
As far as I know, no other browser vendors have committed to implementing Web Components yet, although I understand that Firefox will in the future. Firefox already has support for scoped styles, as does Chrome.
CSS Regions are implemented in IE10 and Chrome, although, once again, the latter currently requires that you enable it using a flag. Both require vendor prefixes on the properties, and IE10 allows only content inside an iframe as the source.
Exclusions are available exclusively in IE10, using the -ms- prefix.
The feature queries @supports at-rule is available in Firefox and Opera, and Firefox also recognizes the CSS.supports() method. Work is underway to bring them to WebKit browsers and may already be in place as you read this.
Cascading Variables are implemented in Chrome only and must be explicitly enabled.