First place I worked at I had several work-friends that eventually persisted to acquaintance+ relationships after I (and many of them) quit. I'm VERY good friends with one of them but the others are people I have no qualms grabbing coffee with but it's a little awkward actually having them over to my house.
Second place I worked at, not so much. I made one really close friend who is one of my absolute best friends, first person other than my husband that I texted in a recent family emergency, etc. There were other people I liked but it would be weird if I attempted to get back in touch for a non-career related reason.
Current job, I have one person who I think would potentially be a friend but my closest contact has been an employee at a client. It was a small-world scenario; she helped her uncle start a the pre-eminent forum for a very specific sub-interest, and my husband happens to be the third top poster on that forum and knows her uncle well. It gave us a head start in getting to know each other and feel safe disclosing about ourselves, so it's been a nice relationship. I look forward to the project being over so we can drop some of the professional pretense and just hang out.