Ditto with jayzher. I think we are discussing two separate things though.  Preparation vs. Warming Up/Relaxing/Getting Out Of Your Head. 

As far as warm ups go my background is strongly rooted in long form improvisation and the group mind, relaxation and trust is critical for me to prepare my cast.  I certainly don't insist on it but connecting with the people you are doing your scenes with and "getting out of your head" seems to work.  Our cast is coming directly from work and or children/family and I think it helps them to shed the day away and then focus on preparation.  I totally respect any way that works for warming up.
So, a couple suggestions that work for me:

Eights - It is mentioned at the top by eveharrington.  You form a circle.  Everyone counts outloud and starting with the left hand counts to 8 by shaking that hand and arm, then you move to the right arm, then the left leg, then right leg.  You repeat the same pattern again starting with the left arm but count to 7.  Essentially this is an energy exercises that helps to change the focus.  I also teach that when you do it you make eye contact with one another and try to smile. 

Another one which I call Pass the Face is a variation of a bunch of warm ups.  It focuses concentration and also relaxes .  Staying in the circle.  One person (person A) turns to the right (person B) and makes a specific movement and sound, then person B turns to C and copies what that had seen passed to them as closely as possible no one should try to change it. It will naturally.  I then add a couple other different moves so that you have to be alert and focus.  So there may be 3 different moves and sounds traveling around the circle.

Finally, I have them stay in the circle and move closely together with their arms down but shoulders touching.  I have seen this work for as many as 10 people so if you have more you should break it up into two or more groups.

So now they have a close, shoulder to shoulder circle.  With eyes closed I have them do a couple deep belly breathes and then when they are ready they will count to 20 one person at a time.  If at anytime more than one person counts at the same time they start over.  This simple exercise is very effective in connecting as a group.  When they do get to 20 they seem relaxed and confident.  If they are really struggling with it I have them take a few more breathes and try again.  I have never seen a group fail. 

All 3 warm ups do not last longer then 15 minutes.

When I perform improv or other shows my fellow performers work on their own to continue their preparation and yes they do all vary but for those few moments they are connected and feel they can trust each other no matter what happens. 

Truly folks I hope I didn't come off as anything but PERSONAL and OPINIONATED for MY OWN SELF.  As I said, I have NO issues with the way other people prepare. I simply do not want to be coerced, forced or threatened in any way to get ME to do those exercises.  Even physical exercise I can handle on my own.  I don't need "the group" thing at all.  If I've done MY job, if they've done THEIR job and the director, SM or anyone else connected to the production do their respective jobs then all should work well.  The physical exercise is dependent upon what the role calls for and how much physicality is involved.  If it's minimal - and at my age now I'm having to do roles with FAR FAR less physicality than when I was younger and more agile - but if it's minimal then there is little to no need to do a bunch of physical exercises.  It's just not necessary if you walk on stage, do your lines and walk off stage. Where's the need?  I do enough to NOT be lock-kneed or stiff-backed, UNLESS the role calls for that. I do enough to remain flexible and loose as necessary.  And as for the lines, I do not need to do a bunch of tongue twisters to be able to deliver what I'm required to say. Now if the line IS a tongue twister or is as difficult, then I may vocalize those lines.  But I don't need to do OTHER than that to get my line correct in that regard.  Seriously, this kind of activity is precipitated, promoted and continues to be pandered to by academia who are dealing usually with a lot of impressionable younger people who 1) don't know any better and 2) HAVE to be given something upon which they are made to THINK they have to rely in order to do their jobs.

Bewdy Toni, very good pionts & also David.
This is where I evaporate & thank gawd I'm just a little black duck, paddling about on the pond. As I don't want or need to emote & prance about on the green sward.
I can't see how you got anyones daks in a twist Toni.

TonyDi--no problems.  I know plenty of people who don't use warm-ups.  I find in my situation (jr. and sr. high school teacher) that these types of things get the students focused and working as a team--breaking through the usual cliques and the natural barriers of grade levels. 

FYI--by the time I get to run throughs we run scales and tongue twisters and then stretch.  The bonding is done and they know how to focus by then.

For those of you wondering about the games I listed before . . .

Broccoli, Tomato--it's a game where they all stand on stage and someone shouts an item.  A motion is associated with the item.  The last person to accomplish the motion is called out and has to step offstage, saying "Thank you, ______" to whoever is calling.  Tomato--hunch over with arms flexed and pointed down in a circle.  Broccoli--stand tall, legs together, hands in fists raised over your head like a broccoli stalk.  There's about 30 of these different things.  My jr. high likes this one better than my sr. high.

Zoom--group stands in circle.  You count in on a four count while snapping fingers (everyone does this).  The person who was designated, on the beat of the snap, looks another player directly in the eye and says "Zoom."  That person on the next beat does the same, but has to choose a different person.  There are variations with "Zip," (to the left or right but not across), "Zap," (turn to the left and the person you actually zapped was the person to your right) and "McFigliani" (skip a person).

Citing the legendary story – which may be verging on theatrical mythology, someone should ask Dustin Hoffman to confirm or deny it – of Olivier and Hoffman’s exchange during “Marathon Man” helps to put this discussion in some perspective.  There are, indeed, many valid ways to get from point A to point B.  If, as an actor, I could reach the heights of either of these great actors, I could probably speak a little more authoritatively on the subject.  Lacking that much talent, I can only use them or others of similar achievement as role models.  As such, they tell me that either approach can and does work.  If that’s the case, I think it is a bit selfish to rail against one methodology verses another.  It is one thing for Sir Larry to bust Mr. Hoffman’s chops and quite another to have any of us at the community theatre level to join in.  In Tony’s defense, on the other hand, this little bit of mythology tells us that at least in that film, there was room for actors to prepare in the way that was most suitable to them. 

But I continue to be uncomfortable with using professional models in an amateur, community theatre context.  Tony referred to “doing his job” and doing so in a most "professional" manner.  This suggests to me that Tony is not functioning in a true community theatre setting, but rather a professional setting.  If that is the case, I have to shrug my shoulders and declare apples and oranges.  I think there is nothing as dangerous to community theatre as trying to incorporate a professional orientation.  The very essence of community theatre means that the talent levels of any cast – and crew for that matter – will and should vary from the greenest novice to the most proficient and experienced artist available.  Given such diversity of talent, using developmental techniques as a director is valid and, I venture to say, required.  I recall a rather stereotypical community theatre actor saying to me once, “I’ve never had a(n) (acting) lesson in my life.”  I didn’t say it, but the first response to come to my mind was, “Yes, and it shows.”  Even at a professional level, artistic development must always be on an actor’s agenda. 

But let’s move on to the issue at hand:  warm-ups.  No matter what level you are – educational, community, or professional – warming up in some form or fashion is critical.  Dancers do it.  Singers do it.  Musicians do it.  As performing artists, why do actors think they are the exception?  And we not only have to warm-up our physical tools (body and voice), but we also have to warm up our mental processes, both emotional and intellectual.  Especially in community theatre, which is a passion and not a livelihood, warm-ups are a critical transition from all the distractions of real life to the focus on fun elements of theatrical life.  How that is done is not up to us as actors; it is one of the roles of the director to decide how s/he will shape the show and run rehearsals.  When I was acting, because warm-ups were so rare in community theatre, I would come at least a half hour early to rehearsals in order to warm-up.  (If that puts me in the Hoffman camp, I can live with that!) 

I think there are two problems.  There are few directors in community theatre that know how to properly use warm-ups and other techniques for the benefit of the show, and there are few actors who know how to properly use warm-ups and other techniques for the benefit of their own artistic development.  I’m terrible at it, but I enjoy playing golf.  When I arrive at the golf course, I usually go to the driving range to warm up with a bucket of balls.  There are times, however, that I’m running late, so I arrive, swing the club a few times, and immediately begin to play.  The truth is, either way, I play equally poorly.  I happened to mention this to the club pro who suggested that I be more intentional in my warm-ups – don’t just try to whack at the ball, but to try to hit it a certain way and try to hit it at a certain target.  I think this is advice that is equally applicable to warm ups in community theatre.  Directors need to know and understand exactly what they want to accomplish by using any given warm-up and actors need to focus on that objective – or some other objective of their own – within the context of the exercise.  My suggestion to avcastner’s original question, then, is that you start with what you want to accomplish and then think of things to do that might work toward that goal.  There are many, many resources, but more and more, for the workshops I run, I tend to make up a lot of my own exercises that are tailored to the needs or desires of the group.