Some really great responses to a really great question!
For me, yes and no. There are some advantages to e-mail (instantaneous communication, for one; not using up paper for another (assuming you don’t print out your e-mails!)), but nothing beats the anticipation of a letter in the mail (and getting something that isn’t a bill or junk mail!), opening it, unfolding it, and reading what someone took the time and trouble to say. Since handwriting a letter takes more time than typing it, it shows the real effort that the writer took, the time and trouble they went to to communicate with you. You can see their handwriting, and their personality is conveyed through that in a way that typewritten fonts never could.
Like others here, letters are also time capsules, especially if still in their original envelopes. I have a box full of letters from friends, relatives, and people now long dead that I enjoy re-reading occasionally. The love letters from girlfriends or letters from very close friends that I possess have a certain familiarity, an intimacy to them that conveys emotions far better than an e-mail ever will.
I have been helping out recently, going through my great-grandmother’s belongings, and I have been sorting through her letters from Paris and New York in the 1930’s, and it’s fascinating both on a genealogical and historical level to read her communications to family, and her observations on a world long gone. The use of slang, the descriptions of daily events, the discussions of postage and how long letters would take to arrive from the point of origin to destination, and the longing she felt for relatives she had left behind remind me of just how much larger the world was before the jet age, globalization, and the internet. That’s something you won’t get from any e-missive.