I'm 37 weeks along now and my husband is in another country, about 16 hours away for work until the end of this week. I made a point not to make too big a deal out of it because I knew that he was playing it cool and not trying to worry himself.
Before he left, we set up a plan of who would drive me to the hospital, who would take care of the cats, etc., just in case. We don't have any family close-by (ILs are 8 hours away) and my family is 6 hours away, but we have several close friends here.
I am also a private person and think that I would only want my husband in the room, but I've never been in labor so who knows if in that moment I'll be fine having somebody else in the room with me. The only person I could even imagine besides my husband is my best pal who lives 3 hours away in NYC who already told me she is dropping everything as soon as she gets the call : )