If you think of humans purely in terms of our biology as defined by Maslow's hierarchy of needs, then no we are not meant to be alone. In purely evolutionary terms, we are meant to find partners to procreate with. I personally think that this is the undercurrent of everything we do whether we want it to be or not. As humans our minds are such that we can prioritise and decide the order that this comes in throughout the course of our lives, but it's hard to get away from, we are destined to ensure the survival of the human race.
Are we afraid of dying alone?
As the chart suggests, we do require more than the basics that keep us alive. I think companionship is one of the most enjoyable factors in life, after all, an experience is nothing on your own, it's sharing it with someone, and sharing and revisiting that memory with someone that really makes it worthwhile.
My personal experience
Having spent from when I was 18 till I was 30 in a serious relationship, spending a year single has been a real eye opener. I used to look at single people and feel pity for them, I assumed that all they must secretly want to be in a relationship - the more they protested they didn't the more I thought they were in denial.
It took me about six months of being single before I even started buying what I wanted for dinner at the supermarket, and not the stuff I used to buy for my husband. Learning to keep yourself happy is really important and far healthier, as long as it doesn't turn into being selfish!
Still ultimately, I don't want to be on my own forever, and definitely don't want to die alone. I think the number of people you have around you when you die is a direct reflection of the type of person you have been and the relationships you have worked on throughout your life.