This is totally IMO...
For starters, it depends on how long the set it. If you're performing for 1 hr+, you could stop in between each song but remember you have a lot of material to go through (and that's what the people came for). If it's a 3 song set (15 minutes), it's more justifiable to stop and do/say something between each song because you don't have much of a chance to show your personality. Anything in between those lengths, you do what feels right.
That being said, there are a million ways to go about your transitions. Some people say nothing and find a way to blend their songs together musically, some tell anecdotes, some just take a moment to regroup their focus, etc. I personally take the last route (cuz it works best for me).
When I go to shows, I find the most effective artists use the element of surprise. If you keep telling stories about each song you're about to play, I will probably lose interest. However, if you tell me a story one time and then the next yell some crazy philosophical phrase into the microphone, it would probably catch me off guard. Tell the audience they look beautiful, do a jumping jack, belch into the microphone if that works for your set. Get weird. Overall, vary what you are doing and make it look like you're having fun doing it. That shit is contagious.