Fear of "NO SERVICE"
I'd fear having no signal if I'm in the middle of a long road trip, but that would be because if my car breaks down, I won't be able to call emergency services.
That said, unless I'm actually expecting someone to call, I sod off the cellphone. Recently I've found out that I can set up my cellphone on a "redirect all calls to voicemail" mode. Guess what I did on my last vacation.
I would have turned it off, but some people who do need to keep in contact can SMS me or e-mail me (few people have my blackberry addy) so I can still get those while sending everyone else to sod off.
As a funny note, I was merely 15 when my dad gave me my first cellphone. I was sick of it 6 months after, thanks to the hourly "WHERE ARE YOU?" calls my dad made every hour after 5pm.