Hi Sara,
Like you I have a lot of photographs of family members taken over different decades which amount to many hundreds, more so now since I obtained a couple of digital camera's. Sometime ago I started to scan all the photographs into the computer that needed doing into different files to be placed on discs. I also have printed off copies of the ones that I feel are important enough to warrant doing.
Having the photographs scanned and then saved onto discs means that I can copy from there instead of getting the original out each time I want one. All the originals I have placed in either photograph albums (where possible) with indivial sleeves for each photograph, or if too large for that they are stored in acid free covers and stored flat in storage boxes safe and away from any light.
The ones that I have printed out I have in A4 folders (again in plastic sleeves) and I use these for reference and it is these that I take with me when I visit members of the family, that way I do not mind if they are damaged or even mislaid/lost as I still have the originals safely tucked away.
Another thing that I have done is that when I have been given photographs by family members not only have I noted who it is in the photograph but also who I received it from (you never know when you might need another copy and over a period of time one tends to forget where the photographs were sourced from).
One other thing, and this should be common practice, don't forget to do back ups on your computer. Not only will you be saving your information and pictures should the worse happen to the computer but it will save you not only the trouble but the time in having to do them all over again.
old rowley