The term hostel has evolved over the last few years. Traditional hostels were known for their meager accommodations, designed for poverty-stricken students and younger travelers trying to stretch a buck. Yet today they have much more to offer the modern adventure seeker.
You can find holes-in-the-wall in any major city, but many hostels are far more refined than you think. Don't rule them out - if you can share a bathroom, you can travel in hostels.
Many locations have options to bunk with multiple guests or offer private rooms. I stayed at a hostel in New York that was safe, clean, and my friend and I had a room to ourselves with no additional cost because of extra vacancies.
On the other hand, you can't always rely on that kind of privacy. If you're willing to surrender a little comfort it's much more affordable to travel abroad with the help of hostels. Ideal candidates are couples, singles, or friends without younger travelers. Hosteling with children is definitely not a wise idea.
Your best bet to find reliable locations is word of mouth combined with these databases:
Next: Hotels