Initially, it was just me. Every once in a while I'd manage to convince a friend to fly out and tag along for a few weeks, thus putting one of those dreaded dates on the calendar, but in a good way. Along the way, I picked up a partner who was doing pretty much the same thing. We've scaled back the traveling a bit recently, but I did manage to drag her around South America for 7 months this year.
I'd recommend going by yourself if you have the choice. You just plain meet more people that way, and you don't run the risk of killing off a perfectly good friendship. On the road, you'll notice the same pattern a lot of times: two English girls who have been traveling together for a couple months and have clearly tired of each other's company but are too polite to suggest they go their separate ways. They're miserable, neither one getting to do what they really want, and forced to eat every meal together even though they've already exhausted all the conversation they could ever come up with. Sit down at their table and you'll instantly have two new friends.
Another benefit of traveling alone is that even as an introvert you'll periodically go into "emergency survival social mode" where you realize you haven't spoken to anybody in four days and you need to make some friends Right Now. And you will. It's as simple as walking up to any random gringo and asking "where are you from?"