As a travel professional and mom of 2 who travels solo with her kiddos a lot (my 5 year old has been to 8 countries, and my 3 year old has been to 6), I try to keep it pretty minimal when we travel, but there are a few things I would not travel without!
The absolute best thing for travel with kids has been a portable sound machine! It's small and light and the battery holds a charge long enough that we've used it everywhere from campgrounds to airports to hotels. There is absolutely nothing worse than a hotel door slamming and waking up a jetlagged kiddo!
For Babies
As a first-time mom, I found the idea of long international flights a bit daunting, but babies who just want to eat and nap are (well, fairly) easy. Bring an insulated thermos for hot water if you're formula feeding - you can bring liquids for babies and toddlers through airport security, though it will slow you down as they'll need to put the liquids in a special machine to check them. You can always fill up the thermos with hot water in the galley on the airplane.
A supportive baby carrier so that I could be hands-free was an absolute must for me. I used our carrier with my younger girl until she was almost 3 for carrying her through the airport - no need to deal with putting a stroller on the security belt, and her head was well out of reach of swinging duffle bags.
For Toddlers
As any toddler parent knows, independence is key for these tiny humans! A toddler-sized backpack that they can pack themselves and be in charge of is great, so they can feel a little bit in control. When my girls were younger, I always traveled with a foldable potty and a foldable stool which I used for helping them reach the toilet, sink, and even for climbing onto big hotel beds!
For Preschoolers
For flights and long car/train rides with preschoolers, I love our Yoto players (not an affiliate link - I just love these) and a nice pair of headphones. My girls love listening to stories and music whilst playing with their sticker books!