Last time I was in SE Asia (Laos/Cambodia), I often had to show my passport when I checked into Guesthouses and they wrote down my details, but don't remember handing it over.
As for motorbikes, there's a lot of Q&A already here you can look at...
Just remember that it's often easy to hire a motorbike even without any kind of bike licence ...*however* you may not be covered by your travel insurance unless you have one. And motorbike accidents are really common in SE Asia! about 7 years ago
Tony, it's not unique to SE Asia, it's also compulsory in Spain, Italy and scores of other countries to register your details and where you're staying with local police or municipal authorities. When you book into a hotel or guest house this is done systematically for you, which is why they need to see your passport, but insist they copy the details and hand it back.
As for motorcycle rental, the primary reason the renters insist on holding your passport is in case there's any damage to the bike they can basically extort money out of you ie if you don't pay you don't get your passport back. There is no legal requirement for you to hand over your passport to Mr Dodgy Motorbike Guy. If the renter needs it only as identification, give him a photocopy of details. If he wants some sort of security deposit, try offering a fully refundable cash deposit instead of the passport.
And I hope you have a motorbike license from your home country, and an international driver's permit, otherwise you'll be riding illegally (see what Christy said above).
More detail here:
Phil from the safety hub about 7 years ago