I most certainly do things at home that benefit my job. Playing with Linux and XBMC etc., setting up an ESX server and learning tricks with it, and all sorts of other hardware related things are all things that I'm interested in. All of that benefits my work too! I've done a ton of work tuning cars plus all sorts of mechanical work and a great deal of just Internet sponging of knowledge as well. ALL of it has benefited me at work at one time or another and I'm fine with that. Nothing I buy for my home is bought just for learning stuff for work however, if I'm not already interested then I won't pursue it on my own time or invest cash.
That said, I work a cool job with interesting people, and I get to play with technology and exercise my brain pretty often - and I ENJOY it. Thus, I love my job! I have known one programmer who flay out stated they "hated computers" and didn't own one. When they went home they didn't touch a computer! They also wrote shitty code and pretty much sucked at their job.
I don't mind researching things for the office and tinkering if I'm already interested but I don't see myself ever not billing if the office directs it and I don't ever work for free. I invest in myself but I don't subject myself to anything boring if I can help it...