I'm not sure I would include HotSPot and other software-based JITs in technologies that allow a processor to improve at run-time. Transmeta's chips are included, though, as they at runtime improves performance of the only architecturally visible instruction set (x86).
Indeed. Transmeta decided not to let the native ISA be visible, so you can not do offline compilation from x86 to this, nor can you replace the architecturally visible ISA. IIRC, Transmeta made a prototype that had JVM as the visible ISA (translating at runtime to the same native ISA as the x86 chip), but that chip was never sold.
As others have mentioned, caches, branch prediction and similar technologies found in almost all modern CPUs will also make the processor improve performance over time, though not as dramatically as the Transmeta chips.
Torben