Most likely, you don't immediately trust everyone you meet on the street or in a restaurant back at home, so don't start when you're on vacation. Sure, one of the advantages to traveling solo is that it's much easier to meet other people, whether they're natives or fellow travelers. But in all places, there are good and bad apples.
You may meet up with other travelers who suggest touring the city together. Before you agree, get to know them over conversation in a public place. Never agree to go to remote locations with someone you've just met.
If you later decide to go to a less-traveled place with them, leave a note with the hotel staff. It should include your description, name, contact information for people at home, passport number (if applicable), destination, names of your companions, and estimated return time. Check in with the staff once you return to let them know you're back.
Don't disclose the name of the place where you're staying, and especially not your room number. If someone wants to meet up with you, suggest meeting in a public place, like in front of a familiar landmark or shop.
Solo travel definitely has its rewards--as long as you use your common sense. If you've made it this far, it probably means you're feeling comfortable with the idea. So on your next trip, go for it, and boost that number of solo travelers up to 9,000,001.