I have a run for the times when they can't free range (if I leave the house). That way they can stretch their legs and still find bugs/worms. They also love drinking out of the mud puddles that form.
Ours were in the run (covered with a tarp) for a long time last winter when we had a lot of snow. We opened the door to let them out, but they hated walking in the snow. I think they would have been miserable without the run during that time.
I have a run because that's how I started, with too many fears to let my chickens range freely. I got my first chicks in October 2009, and wasn't brave enough to let them free range until a month ago. I ONLY let them out of the run when I am home! And, actually, their "range" is just my entire back yard, which is very large (about a quarter acre). They don't get out onto the larger property on which I live; just stay in my back yard. So far. They haven't breached the back yard fence yet.
So, they're out every weekend, and every other weekend for me is three days. Sometimes I let them out when I get home from work in the evening, but that's not a regular practice yet.
Having a run is definitely a plus here in Texas where you never know what the weather will do. We keep ours in the run/coop while we are working and let them out in the late afternoon. They are out when we are home on the weekends as well. I don't know what we would have done without the coop and run when we got all the SNOW?! in January and February!
I have a good sized run, and mine can roam our 3 acres when I'm home. When you spray for weeds, have company over, or do certain types of lawn or outside maintenance, it's nice to be able to keep them contained for a few hours (or days even) in the run. However, some folks strictly freerange and it works for them...
I have a run, too - for all the above reasons. Weather, company, vacations, etc. It's important for them to still have somewhere to move about when they can't be out.
Of course, they only spend an hour or two in it in the morning before I get up there to let them out. Then BAM! They are all out the door as fast as their little chicken legs can carry them.