The obvious advantage of traveling alone is that you and only you determine the daily schedule.   There are no compromises to be made and no adjustments for anyone else.  I can remember traveling in Paris and Italy and covering a tremendous amount of ground in just a few days that would have taken me much longer if I had been traveling with a partner.  I also enjoy the sense of anonymity and freedom.

In terms of safety, I think risks increase a bit when traveling alone in Europe.  Let's face it, there are some bad people out there and I get the feeling they will target someone traveling without a partner before an accompanied traveler.   Therefore I would tend to always stay with a crowd, be ultra careful at night doing things like eating at the hotel restaurant instead of scooting across town.   I am hesitant to enter a public restroom unless there is an attendant or other people in it.  Unfortunately, women traveling alone must be even more careful.

The other issue that bothers me when traveling without a partner is dining.  To solve that, I would go to the well-known Jim Haynes dinner in Paris to meet other travelers.  See:  http://www.jim-haynes.com/

I have also posted on sites like TripAdvisor and craigslist to look for dining companions when traveling alone.  However, I urge caution when doing so - only meet in a public place with a group of people.

Churches and other similar organization often sponsor meetings and group dinners.  I have always felt welcome there.

I think the reason my travelers like my small group tours is that the itinerary is flexible and we always plan a group dinner every night.   Lots of people say a touring situation like that is just what they were looking for.