I thought that it's pretty common for companies to ask for references and / or testimonials. Isn't there always a section in Application Forms for you to provide references?
I have heard of companies who actually call up your references, or your previous employer, to ask them about things like your punctuality, reliability, character integrity, etc. I've heard too, that there are HR personnel enlightened enough to not ask your previous employer about your job performance because they acknowledge that some employers might be petty about your resignation and might jeopardise your new job by trying to provide a less than glorious testimonial.
It's always good to ask for a testimonial from your bosses after you've tendered your resignation, and before you actually leave the company. I always try to do that although some bosses would promise you that they'll do so, then they'll 'forget' because they're 'too busy'.
One of my ex bosses even said, 'You're so good at composing documents... could you submit a draft for me and I'll add on or edit that?' when I asked him for a testimonial!
I laughed it off... but now, I wish I hadn't!