I have a Core 2 Duo machine running Elementary I break out once a month or so since it has some cool synth software on it. It's totally usable for me, and that's with a pretty bloated OS compared to alternatives.
Sure, for specific applications, almost any computer could still have a useful purpose (hence me reusing my T61 for a router) but we are talking about a daily driver here. In my case, browsing the web became noticeably slower, especially watching videos. I began to suspect my CPU/Intel GPU lacked native support for decoding some newer video formats, but I don't know for sure. This is where its age really began to show though.
> synth software
I use a 2008 MBP 17" because I have legacy versions of music production software that costs a lot, that I can no longer upgrade. It runs great, but it has an occasional memory buffer overload when trying to record and playback too many tracks at once.