Eduardo Lima Mitev of Igalia posted a set of 65 patches today for implementing ARB_internalformat_query2 support within core Mesa and is implemented then within the Intel i965 DRI driver.
While as a user you might not care what ARB_internalformat_query2 is about, it's significant that this is just one of two extensions needing to land in Mesa Git before core Mesa will have OpenGL 4.3. Assuming this big code review goes well for this extension work done by consulting firm Igalia, there is then just the GL_ARB_robust_buffer_access_behavior extension blocking OpenGL 4.3 exposure.
While hitting these two extensions will mark compliance for core Mesa, the actual hardware driver state varies. Igalia implemented the ARB_internalformat_query2 for Intel (as they are in a business relationship), the Intel driver just needs ARB_robust_buffer_access_behavior, so will presumably reach GL 4.3 when that extension hits core Mesa. However, the Intel driver still needs OpenGL 4.0's ARB_gpu_shader_fp64 and OpenGL 4.1's ARB_vertex_attrib_64bit extensions to catch up. (All OpenGL 4.2-specific changes are already complete on the Intel side.)
The RadeonSI Gallium3D driver is at OpenGL 4.1 currently but lacks ARB_shader_atomic_counters and ARB_shader_image_load_store support for OpenGL 4.2. After that, there are seven OpenGL extensions needed for RadeonSI to hit OpenGL 4.3 compliance. R600g is in a similar boat, but there only the Radeon HD 5800/6900 series support even OpenGL 4.1 right now due to having real FP64 support.
The Nouveau NVC0 meanwhile is slightly ahead of the RadeonSI state thanks to recent advancements, but they still have a lot of work too before calling themselves OpenGL 4.3 compliant. MesaMatrix.net has the nice overview.
Mesa 11.2 is set to be branched from Git later this month. While it's possible that core Mesa will meet all the OpenGL 4.3 requirements before then, the Intel DRI driver will still likely be blocked by the FP64 support unless that code really gets wrapped up and lands in the next two weeks. On the Radeon and Nouveau side, perhaps we'll see OpenGL 4.2 working in the next two weeks, but it would be a huge miracle if all of the OpenGL 4.3 work was magically completed in time for Mesa 11.2...
Thus this moves the OpenGL 4.3 target out three more months per Mesa's usual release cadence. So hopefully by this summer there will be Radeon/Nouveau support for OpenGL 4.3, assuming you're on a rolling release distribution or are comfortable in using third-party repositories or building Mesa yourself, otherwise it likely won't be until this fall when you'll see out-of-the-box OpenGL 4.3 support on the Linux desktop. During that round of distribution updates too is likely when seeing the first out-of-the-box Vulkan support as well. Beyond OpenGL 4.3, much of OpenGL 4.4 and 4.5 is left to be accomplished.