Old correspondence is usually referred to as ephemera which relates to things that were made not to last such as letters, postcards, greeting cards, etc. While old letters can be a wonderful window into your family as well as history, there is not much value in ordinary correspondence unless it is from a significant person or relates to a significant event. You can find old letters for as little as one dollar.
Do not store your letters in the attic or basement. Avoid storage areas with extremes in temperature or humidity. Keep your old letter in acid-free folders or in archival quality polyester film (not Ziploc bags).
If these letters are from people in your family, you should keep them to hand down as a wonderful keepsake and family history.