Hotel Search Engines

Are you referring to a hotel search engine? Please specify what you are looking for.

Oops, I see your title. Pardon! I always begin with Booking.com and have always been happy with their site. Easy to navigate and their reviews can only be from people who have stayed there, unlike Tripadvisor. You can always contact a hotel directly if you find some place that interests you and you are looking for a better deal, perhaps. Customer service with Booking.com has always been prompt and satisfying, in my experience, and when needing to be in touch with the lodging, their system has always been good. (P.S. I don't work for them...just happy with their service/product over many years.)

We, too, rely on booking.com to research our accommodations. Their filters allow you to narrow things down quickjly with regards to location, pricing, amenities, etc.
Once I've narrowed things down I usually check the individual hotel's website - can sometimes find better pricing, a more relaxed cancellation policy, and better amenities by booking direct.

We usually use either Booking.com or Hotels.com.
Both have been reliable resources for us.

Thanks to everyone for the quick and thorough responses. It helps.

Judy

I've sometimes used a motel chain website in the US, but I've never used a 3rd party booking site, like Booking.com, here or in Europe.

I've done studies of booking websites in a number of towns I've stay in in Germany, and I've always found that the places shown on Booking were amongst the priciest place in the town. I mostly use the town tourist office website to look for accommodations. I don't deliberately avoid places listed on booking websites; a few times I've ended up at places bookable with Booking.com, but by going direct to the properties website, I've always gotten a better deal than I would have gotten from Booking.com.

Booking in the US and Germany are entirely different "animals". In Germany, places like Pensionen and Gästhäuser are mostly independent businesses, not national chains, and nice places. Here, it seems that most motels belong to national chains. In Denver, independent motels are mostly on Colfax (the main street through Denver. US 40, I-70 Business) and rent by the hour, if you know what I mean. Not just Denver; same for independent motels in other US cities I've lived in.

fyi,
Booking Holdings Inc. owns and operates Booking.com, Priceline.com, Agoda, Kayak, Cheapflights, Rentalcars.com, Momondo, and OpenTable.
Expedia Group, Inc. owns and operates Expedia, Hotels.com, Vrbo, Travelocity, Hotwire.com, Orbitz, Ebookers, CheapTickets, CarRentals.com, Expedia Cruises, Wotif, and Trivago.
Tripadvisor's other brands include Bokun.io, Cruise Critic, FlipKey, TheFork, Holiday Lettings, Housetrip, Jetsetter, Singleplatform, Niumba, SeatGuru, and Viator.

Here's a current thread with some pretty severe criticism of booking.com, at least as it relates to short-term rentals. I use it to help find hotels, with useful filters and genuine reviews. But I book directly with the chosen hotel, not through booking.com. I'd rather deal directly with the business than through a third party that may not be responsive if problems arise.