In the session I run (around the room not floor spots) the one big comment we always get is that people do enjoy the diversity of it.
I am the only singer/songwriter (i really do dislike that moniker) there most weeks and the session is primary a folk session with the odd person doing something different, I'd say it's pretty much 80% folk on average.
Before I took it on it was run by a chap who did blugrass and all and sundry assumed it was a bluegrass session as he would bring his band down and do three songs in a row leaving the rest of us round the room shuddering under this 15 minute saturation of bluegrass every few goes. As a result attendance dropped off and folk performers were put off coming to the session as they didn't view it as a place where they could listen to, play and learn new songs or varients of songs in the folk tradition.
So, when i took the session over I made the point of going to other sessions and talking to people, making the folk contingent feel welcome, getting unaccompanied singers into the room and encouraging good chorus songs and people who had previously left the session to return.
As an acoustic singer/songwriter (urrgh) in the, i guess neo-folk, alt-folk genre (labels, labels...)it is often quite daunting performing in more trad based sessions that are 'unfriendly' to musicians like me as I feel people who are writing in the tradition but in a contemporary way are often ignored or dismissed as the generic singer/songwriter and some very good music can go unheard because of this sort of attitude. I do also perform trad songs, arrange some to my own interpretation and collaborate both musically and vocally in the old school sense of trad which I view as just as relevant and exciting to perform as anything I do in the contemporary self-penned sense, often moreso because, for want of sounding hackneyed and cliched, it is breathing a new burst of life into a song again and perpetuating that music and the history contained within it. Indeed, I often have weeks where I'm just doing trad or just doing unaccompanied singing.
My point is I feel that my session succeeds because I welcome all people, want everyone, even the listeners, to get involved in the music and the fantastic goose-bump lifting atmosphere created by a whole packed room of people doing chorus on a shanty or the like and don't make people like myself feel unwelcome because they happen to want to play a song they have written in a session. You never know, they may find some inspiration like I did in the folk music they hear and turn up next week working steadily from Child #1 upwards.

One more point (forgive the lengthy post) remember to talk to newcomers, ask their name, make sure they have an oppertunity to play and hopefully they will feel welcome enough to return to the fold.