There's no absolute in this. Some companies will pay for your training/certification and have you do it on company time. Others not. It really depends on the company.
I'm fortunate enough that the first option is pretty much always what happens for me. But it's entirely because of the type of company I work for. I'm a storage engineer for a big data center VAR, so I need to be up to speed on a huge number of different storage systems. The company gets financial incentives from the vendors to have employees get and maintain those certifications. The more of us with certifications from a particular vendor, the bigger the financial gain for the company. I take as much advantage of this perk as possible, and I'd suggest that anyone who can get their employer to pay for training jump on it. It makes you more valuable to the company, and in the job market in general.
Whether any of those certification is worth the paper they're printed on is a completely different discussion. :)