A couple of years ago, I hit a genealogical jackpot when my grandmother opted to downsize, and offered me all of her photo albums. And I do mean all. Collectively, they document everything from her parents' youth (the 1900-20s) to my early 20s (the 2000s). 100 years of photographic history - every genealogist's dream. The problem was, no one knew who half of the people in these photos were. We could pick out my great grandparents easily enough, and even my great-great grandparents, but there were countless full-family photos, such as the one above, that left us all perplexed. The eldest woman in the photo is Ann Arnell-West, who is not actually related to us by blood - she was the wife of William West, father to our ancestor Minnie West - but Minnie's mother was William's short-lived wife, Mary Taylor. The names of William and Ann's children are known, but no one has ever been able to tell me definitively who the people in the picture are.
Where do you turn, then, when you find these fantastic images, but have no names to give them? There are a few online sources that have helped immensely. AncientFaces is probably the largest database of genealogical photos online today. If you have any idea what surnames may be found in said photo (for example, even though I have no idea who is in the above picture, I can be sure at least one of them is named "West"), you can search for that name on AncientFaces, and both seek out familiar faces, and connect with others researching that name. FindAGrave is also a great resource - while it focuses mainly on gravestone photos, many members add portrait photos as well, so if you have any inkling as to who the people in your mystery photos may be, searching their names on FindAGrave is an excellent idea.
Another tip I will offer probably will not sit well with my fellow skeptics, but I hope you will hear me out on this. Learn to trust your instincts. Yes, we all want empirical evidence that these people are who we think they are, but there's something to be said for really just looking at these people. When I lay pictures of my mother, her mother, her mother, and her mother beside one another, the resemblance, the blatant similarities, are impossible to deny. I can see my own face in my great-great-grandmother's, I can see my father's face in his great-great-grandfather's. If you have mystery photos, I strongly suggest playing detective, and examining each and every face closely. It took me only a little study to place my great-great-grandfather, whom I'd never seen, in several of the photos my grandmother gave me - a little common sense, and a bit of facial examination, made it pretty obvious that the older man seen in photos with my great grandmother Dorothy, that looked an awful lot like one of my great uncles, was most likely Dorothy's father.
But what do you do if you have no picture - just a name? Look to the internet, of course! Desperate times call for desperate measures, and I've had astounding luck just Googling my ancestor's names, or turning to forums dedicated to a specific surname - GenForum, Ancestry.com, and Facebook are all good places to start. In our research, we have to keep in mind that surnames are, historically, actually a fairly recent invention. Depending on your ancestry, you may very well be at least distantly related to pretty well everyone that shares that name. Perseverance is the name of this game. Google every name, search for images, follow every lead. FamilySearch is a valuable research tool in this situation as well. You can search by name alone, or add locations, dates of birth or death, spouses names, parents names, or any other information you can come up with. Even guessing pays off now and then - I don't know when my great-grandfather was born, but I can guess, based on my great-grandmother's age and my grandfather's age, that it was probably between 1900-1910. Entering that date range narrows down the search results dramatically, making it easier to find likely candidates.
The best advice I can give is the most obvious - don't give up. Try every variation of their name that you can think of. Search for their brothers and sisters if you can't find them. Dig through virtual graveyards, search Facebook for groups dedicated to those families, post in every genealogy forum you can find, Google each and every name, email anyone that has listed their address online. Examine census records, search Google Books and libraries for references to their names, look up the histories of the cities they were born in or moved to. It is amazing what you will find if you look hard enough.