Time is a fluid thing, and not just in physics. For a band time is fluid in the regard that a venue may grant a little more time or a little less time on stage than originally planned. Why do I mention this? I recently saw a band who announced onstage that it was granted more time than it had planned on. Normally, this would be amazing news for a band. However, this particular band didn't seem prepared for it. Don't get the wrong idea here. this is not an ultimate survival guide for every potential situation. These are merely some suggestions for being prepared if your allotted time on stage changes. After all, this is your time - no matter how many minutes it is.
Learn some covers
I realize that when you rehearse with your band, you practice just like you'll play at the venue. That being said, if you are given a little additional time for your set, some covers are a great way to fill that unplanned time. Sure, you want your band to be known for your original material, but playing some covers in this situation will only make your show more memorable for fans. Think about it. It's a good thing if some people are seeing you for the first time, but they're still singing along with you. You need not sacrifice any artistic integrity because you played a couple covers during your set.
Maybe this is not as easy as I'm making it sound. However, if you're in a band with people - even if you're not a jam band - you should have the ability to improvise for at least a couple minutes. Let each member of the band have a solo. That will fill some time, and prevent you from having to tell rambling stories just because you weren't prepared for the time you now have to fill. And if you don't feel like you can improvise, just remember this story. I once saw Ray Charles on Letterman's show, and Ray said that the song "What'd I Say" came about one night when the band had played all of its material but still had time to fill. He told the musicians and backing vocalists just to follow what he did and "What'd I Say" was born.
Conversely - and this is the more likely scenario - what do you do if you show up at the gig and you're told you have 35 minutes instead of the 45 you planned? Everyone in the band should know which songs to drop from the set to accommodate the shorter duration. Sure, it's lousy that you don't get to perform the whole set you planned, but you just have to go out on the stage and be just as effective with less time. Maybe these things aren't sexy things to think about, but they certainly are things you need to consider when you rehearse with your band. Just like any Boy Scout, you need to be prepared. After all, if you're prepared and professional, the folks at the venue are more likely to invite you back.