I'm pretty much the "on-call" guy here at the plant for programming and controls items for support by phone, but it's not a mandatory thing. I'd rather someone called me and asked about something BEFORE I have to head into the plant to fix something they messed up.
But... Being single and having a fairly active social life..... I tell them to FIRST find out if I've been drinking that night.... If the answer is yes, then they get to call my boss and wake him up instead of talking to me. The rest of the time, I'm a night owl by choice, so a 3 am phone call normally just interupts my computer gaming time.....
If it's not something I can clear up by a 5 min phonecall, or if it takes a skill set that the people in the plant haven't used yet, then I usually head into the plant and take care of it. I only live about 10 minutes down the road from the plant, so it usually isn't a big deal for me to head in(unless I have company, or am otherwise occupied). I get 4 hours min pay for actually going into the plant, whether it takes me 5 min or even if the guys on shift figured it out before I showed up. If I spent too much time talking on the phone to someone I could get paid for that too(I guess), but it's never come up so far.
I guess if I was minded to abuse the system I could, but my boss is fully aware that I'd rather have the time off than the extra money, so there haven't been any issues in that area.
I don't need to come in nearly as often now as I used to, because anytime I do get called in to help out, that just pinpointed the next area on my training schedule for the maintenance techs.