Rick said:
You would be much more aware of your surroundings and you would tend to travel more comfortably (at your own pace) and see an awful lot more wildlife.
In reading this thread, I can't add much to what has already been related other than to really emphasize what Rick and others have said. Awareness of surroundings is the factor that draws me and is most enhanced when solo. Probably 90% of my hiking these days is done solo, mostly in the western half of the Adirondacks, bushwhacking off trail between small ponds. A cell phone is pretty useless there so I don't bother with the baggage of it. I enjoy more than anything detailed observation of the wilderness, all senses are wide awake and enhanced as I learn the lay of the land of where I have been, where I am, and where I intend to go. Leaving the GPS at home on those trips removes the temptation to "cheat" and ignore learning nature's own navigation clues with my own wits.
My solo memories are made up of thousands of small events that would certainly go unnoticed if I were hiking with a partner. It's just different that way, amazingly different and wonderful. Every step is more thoughfully placed than when chatting with a partner. When less experienced, that little inner twinge of feeling alone and a little (or a lot) unsure of where the map & compass put me - then stopping to sit, have a snack, observe the terrain just past and think it through of where I must be. I can recall to this day the details of many of those past feeling "lost" experiences and the exact log or rock I sat upon. Oh, gosh how could I forget the time of a cloudy day when somehow my compass dial got itself turned by 30 degrees while crawling through a thicket, not to be noticed until the other navigation mismatch clues began to add up almost an hour later? Sat down to think about that one for a long time, cherish the lesson it taught me about questioning early when observations accumulate that don't quite make sense, smile about it years later. Learning from those days is one reason today why I do not wish to or have need to carry a GPS.
Then there was that foolish handhold I knew I should not have trusted that sent me tumbling unhurt but scared - I can still feel it give way in my hand, and I'll not do that again. The first view of the shining lake approaching through the trees after a too long solo bushwhack slog. Which way is the wind blowing, why did it change direction and what do those clouds mean? Where is that ravine, is that rising ridge supposed to be there? There was the time I lost my sleeping bag and retraced my steps to find it just before freezing darkness - I'll never forget the details of that one. And the moose and calf I came upon silently without startling... All great stuff of the mind that would be far different or nonexistent when hiking with others. I enjoy those kinds of experiences but know they are not for everyone.
My greatest fear always is breaking a leg or worse in jumbled blowdown. Not much I can do about that other than to know when to back off when tired, not take that leaping chance, to stick to my itinerary (or the discussed backup plan), and trust I am on track with my whistle ready in my pocket while waiting for help to come in a day or so. As is true with anything short of staying home in bed your whole life, I guess that's the risk you must be willing to take and weigh the value of the rewards to you and risk to your family.