Depends on factors like vacancy rates in your area.
How do you overlap if the place you have now is month by month, and the place you want to move into isn't available until the 1st of next month? If you give notice, you have to move out the morning of the 1st, unless you pay another month's rent, and only on the 1st can you get keys to the new place.
The only way you will get overlap is if the people move out of the new place sooner and the new landlord lets you start moving in, or else your current landlord doesn't find any new tenants for the next month and nicely agrees to give you a few more days to move out.
When vacancy rates are low, the good places you want are never the ones that are conveniently vacant: what you want, everyone else wants.
It's not unheard of for one group of renters to be moving in simultaneously as another is still moving out.
In Vancouver, Canada things must be quite dim in this regard these days. Check this out:
Ouch! You're not likely going to find a nice, empty, move-in-before-official-date apartment here in this market.
By the way, from the above: "citywide, two-bedroom rents jumped to $1,643 from $1,571 in 2014." I haven't been looking, but the 2014 figure substantially surpasses my current mortgage payment plus property taxes and maintenance fee. Bye bye!
Places I rented never had the period starting on the 1st. Maybe that's a standard somewhere else, but I didn't experience it in the UK. It seems like a nightmare to both the renters and landlords...
Not exactly randomised, just available when they're available. It normally looked like this - my current rent ends on the 10th of March, found a new place to rent and say "here's the deposit, I'd like to move in on the 5th of March, ok?" and everyone's happy.
In a college town like Boston, many (most?) of the student rentals turn over on Sept 1, so Aug 31 and Sept 1 are an utter shitshow, especially when mixed with the inbound collegians, and the inevitable dim bulb who decides to stuff their moving truck under one of the bridges on Storrow or Memorial Drive.
When I was renting, I always tried to get a few days overlap, but in some markets it's very difficult. After all, if I'm moving into my new place on 9/1, you can't very well move into my place a few days early, and vice versa.
Why do they do that? I always took at least 3-4 days overlap between the rent on the old and new place. Assumed that's what normally happens.