Ever since the internet came into existence, my sister and I have done our bookings online. Up to now we never had a bad experience.
Of course, you need to be careful. Some online offers seem to be good to be true, so it's best you stay far away from them. That is the main reason why I don't put a lot of trust on sites like Booking.com or any other site that offers hotel stays. Too many times I've heard from people who had made a booking through one of these services, then arrived at the chosen hotel to hear there was something wrong with the booking - or once the hotel even didn't exist anymore!
I prefer to book directly with the hotel. When their prices vary from those of the likes of Booking.com, just mention you've seen a better deal. They'll lower their price as well. Also, with hotel chains, loyalty pays. We often stay at Hilton hotels and this way we built up a nice sum of points. With them, you can book a stay for free! We've already had a free 4-day-stay in Amsterdam and more recently we had an entire suite for free.
When you want to book airplane tickets, it's like a game. For overseas destination, it's good to book about 10 months in advance. You'll pay directly for the tickets, but they will be way lower than when you book later on. For instance, we had a look at the airfares for Buenos Aires. At the moment we looked the lowest fare was 2,400 € for two people. That was in 2015. But when we actually booked the tickets earlier this year, we only paid 1,700 € (including annulation insurance). For flights in Europe, you just have to wait until the airline announces a reduction. Sometimes you can fly to destinations inside Europe for just 39 €! Beats Ryan Air. We mostly travel with Brussels Airlines or any other airline that is in the Miles & More program. For 10,000 miles you can travel for free.
Care to share your experience with online booking?