"What do I do if he falls?"
I hike by myself fairly often, many times in trackless areas. Lots of people ask me "Is that safe? Shouldn't you hike with somebody else?" Given my engineering bent, here's my analysis:
One person - nobody to blame but yourself if you get in a tight spot. As another author (John Dowd) said, solo journeying is the ultimate in personal responsibility. Most people tend to be more cautious when they know they're lacking a safety net.
Two people - I maintain this is the most dangerous configuration, especially if both hikers are male. Two people usually have the dynamic of egging each other on if the group gets in a tight spot. All of my closest calls in the Sierra have been when hiking with one other guy. If something bad happens and one is injured (you've REALLY screwed the pooch if you manage to both get injured at the same time), now what? Imagine the anguish (this happened to me) of seeing your friend on a steep slope far above you, stuck, calling for help, as you're thinking: "What do I do if he falls?" Does the uninjured hiker stay with the casualty or hike out for help? If you choose to hike out, guess what? You're now a solo hiker who's mentally traumatized, probably tired, and in a big hurry. Bad combination...
Three people - OK, now it makes a bit more sense, in that there's no need to decide whether to stay behind and aid the casualty or to hike out for help. But still, the one going out for help is a solo hiker! Hopefully the one hiking out for help is the most-cautious and level-headed of the three.
Four people - Hah, that's the ticket. Now, if one person is incapacitated, one (the one with the best medical skills) stays behind and the other two hike out for help. But now ask yourself: in the modern world with everybody having multiple jobs and responsibilities, what's the likelihood of being able to find three other people whose schedules coincide with yours? Small. Three others who hike at the same pace and have the same skill level as you? Smaller still. And the kicker: three other people who satisfy the previous criteria and with whom you are comfortably compatible in the wilderness for several days? Pretty darned small indeed. So: should you stay home, or go hiking when you have the time? I say, GO HIKING. If you can find a group, great; if not, GO ANYWAY.
Any hike, no matter the party size, should have a trip plan that is communicated to a responsible adult back at home base who knows the correct authorities to contact if you don't call in at the appointed time(s), whether mid-trip or just from the exit trailhead. Having a plan and carefully trying to stay within its boundaries is survival-enhancing.
Some have pointed out to me that there are now cell phones, satellite phones, and personal locator beacons (EPIRBs) to enhance rescue success. Cell phones are seldom useful in wild areas since you're out of coverage in many places. Sat phones and EPIRBs certainly are a good, if costly, development as long as they don't act to make you take more chances. I now have and use a SPOT tracker. That device even allows me to configure a web page showing where I've been recently if I so desire. But I maintain these devices are neutral to the dynamic I discuss above: a sat phone and EPIRB make as much or more sense for a group as they do for a solo hiker.
Finally, there's the reality that hiking by yourself is just a different experience than hiking with a group. I think every hiker should consider that they're missing out if they don't sometimes hike by themselves AND sometimes hike with others. Solitude, companionship: try them both.
For some additional perspectives on solo hiking, try these links:
Charlie Hayden's 2002 hike (search on that page for "Solo Hiking".)