Numerous Phoronix articles in the past few years on LLVMpipe have shown how its performance is slow and obviously can't compete with dedicated graphics hardware. However, that's not meant to be its purpose. The LLVMpipe driver began an version of Gallium3D's Softpipe driver that is faster for handling OpenGL due to its use of LLVM and its optimizations. LLVMpipe is used by graphics driver developers commonly in testing Gallium3D changes and debugging other OpenGL drivers in having a common, open-source, hardware-neutral driver for validating changes or regressions. It's a decent OpenGL reference driver implementation if performance isn't important.
More recently, Gallium3D's LLVMpipe driver has expanded greatly as a fallback driver on the Linux desktop in cases where no OpenGL hardware driver is available. With desktops like Unity and GNOME Shell needing 3D/OpenGL support, LLVMpipe is a last-step for supporting them. The performance there at least tends to be "good enough" on recent CPUs for handling modern desktops -- it's certainly much better than Softpipe or the classic Mesa Software Rasterizer.
Matthias Hopf, the X.Org developer who previously was at SUSE working on RadeonHD and X.Org that then left to become a professor in Nürnberg, shared during XDC2013 how he uses LLVMpipe in teaching. His presentation this week on Portland was about "Thoughts and Experiences with the OpenGL Software Rasterizer."
Matthias Hopf pointed out that while Mesa's OpenGL support (OpenGL 3.1) is four years behind the latest upstream spec that's now up to OpenGL 4.4, it's the GL Shading Language features lacking from Mesa that's hurting him most in his uses.
In his teachings at the university in Nürnberg, Hopf has found it best to use the Mesa Software Rasterizer (LLVMpipe) due to different OpenGL versions being supported by different Mesa/Gallium3D drivers, behavioral differences between the drivers and graphics cards (not attributed to Mesa alone), and different bugs being present. Given that university students are generally just rendering simple shapes and figures when learning OpenGL and 3D rendering, the LLVMpipe driver is good enough in terms of speed and features while allowing all students to run from a common driver code-path.
Matthias Hopf expressed that even OpenGL shaders (GLSL) is now becoming "reasonably fast" thanks to leveraging LLVM. What he's wanting to see most out of LLVMpipe right now though isn't OpenGL 4.4 but just GLSL 3.30 support (the shading language that's part of OpenGL 3.3) due to it being easier for handling attribute binding.
That's about it. Those students or professors thinking about LLVMpipe can see Hopf's PDF slides.