We use Dropbox.
Even our guitarist can access them (and you won't find a bigger technophobe than him).
TL;DR
Record rehearsal/gig on handheld recorder as .wav file
Transfer files to PC
Edit out individual songs
Convert to .mp3
Copy to Dropbox
Long version
I use a Tascam DR-40 stopping the recorder every few songs to keep file sizes manageable, taking notes of what songs are in which files. The better the notes I take the quicker the editing is.
I upload the files to my PC and edit out the best take (using Audacity) so you don't have to listen to all the chat. Starting at the last file (for rehearsals) and working towards the first as the best takes are usually the last ones.
I then convert the individual .wav files to .mp3 (using Sound Converter), put them in a folder titled Band_Name_YYMMDD (date in reverse order so they appear in chronological order).
Lastly I copy this folder to Dropbox. Don't drag and drop it because another band member my drag and drop it from their Dropbox folder so deleting it from Dropbox. (Our drummer did this the first time but I had kept a copy.)
Hope you followed all that. It took me a while to get the method sorted out but now editing a rehearsal or gig takes me a few minutes.