I've been involved in design of an ASIC that used a customized Tensilica DSP, circa 2009. The custom instructions were the main reason we opted for that core. There are a ton of other customizations that you can make with Tensilica so you end up with a core that meets 100% of your needs with very little fluff -- almost as if you rolled your own.

I do wish ARM would get in on that action.

Radeon R600 (HD 2000/3000 series) also used xtensa as an embedded controller and Unified Video Decoder

The "add your own instructions" thing is a pretty cool, no doubt. I would be surprised if most ASIC designs really really need the low latency that provides, especially considering the other costs involved in adopting a minor-league ISA.

They do... the Cortex A/M coprocessor scheme can be used to add instructions & functionality IIRC.