Booking.com

Alternative dates are often offered if the required dates are not available, you do not have to accept them.

Generally hotels only put a percentage of their vacant rooms on booking.com that's why there were rooms available when you rang the hotel. Booking com staff only see their allocation so the hotel would appear full to them, they work for booking com - not the hotel - so would suggest different dates or different accommodation rather than suggest you ring the hotel to check.

Always best to research on booking.com and then make the booking direct with the hotel if you can. Be aware of price differences, booking on booking.com may be cheaper than booking direct.

We are abroad using them currently and finding that when we go to book and pay, are told to try again which we do, only to find the price has gone up!!

I booked my entire holiday in the UK last year via booking.com, stopping for 1,2 or 3 nights in different hotels over 2 weeks in the North East. It all worked out perfectly. I was communicating with most of them through the booking.com messaging system in the run-up and had no problems at all. In fact, I have never had a problem with them. I do sometimes book directly with the hotel having found them on booking.com but have never found a difference in price although I expected to. However, I will be extra careful in future.

We have used them many times over the years. Only had an issue once and that was the accommodation being greedy due to an event being on in the area. It turned out to our advantage as we managed to book an alternative place. This was also with booking.com but rather than a hotel room it was a delightful ground floor studio/garden apartment a few minutes walk from the event. In fact we have booked to stay at it again next year.
You just need to take care when booking.

I use them frequently, you do need to take care with dates when booking, but so far, touch wood, haven't had any mishaps, I've reached "Genius" level with them which supposedly gives a discount. I often check as to booking with the hotel direct to see if it's the same rate, as mentioned by Jacky above, that usually appears to be the case.

I use them several times a year...never had an issue

Have used before without problems but much rather book direct with hotel, generally cheaper and they don’t have to give booking.com a cut.

I've used Booking.com for hotels a lot, and Airbnb for apartments without any problems. However, I think Booking.com is probably open to scams on apartment rentals/homestays. As I've described on another post, I booked a place in Paris, which seemed to be a room in an apartment, but was only contacted by owner the day before "reminding" me that it was a homestay and that there was a curfew - no entry after 7.30 pm every night!
Next day, he more or less cancelled - "wife had a tummy bug" and offered full refund, which I've got.
I've since found the identical property listed on Booking.com with another title, same address and photos but no curfew conditions and some different facilities.
There were few reviews on either listing- most very positive but one saying they couldn't get access and 2 said they cancelled when they found out about restrictions.
I suspect the apartment doesn't exist- waiting response from Booking.com but at least I've been refunded.