I don't have a mobile phone and rely on my laptop to be contactable. My experience is I'm not much less contactable, because I'm seldom away from my laptop for more than an hour at a time (unless I'm asleep), and I respond to emails/ Facebook messages / Skype calls etc quickly. The only real disadvantage I've found is when I'm moving around with no access to an internet connection, but even that can be worked around - after all people did that all the time before the advent of mobile phones.
Not having to pay for the phone's data plans has saved me thousands of dollars over the years; however many people keep telling me I should get one because of how indispensable it is, including in job searches.
Does not having a mobile phone disadvantage me in the job market?
Re country: I'm not keen to say which country it is (especially since I might move around in the future), but it's one in which most people have mobile phones, and there are no prepaid cards (the kind where I pay $10 for ___ megabytes of data and can use it until it runs out, when I top up another $10 -- which is the only kind of plan that makes financial sense for me given my usage).