I wouldn't say I really have one item I consider my 'favourite' item of travel gear but I do have several items that I wouldn't travel without.
The first is my trusty Swiss Army Knife. I can't count the number of times this has been the solution to dealing with something while I was travelling. I once used it to re-attach the sole of a hiking boot to the upper by using the awl to make holes in the sole and then use snare wire to re-attach the sole to the upper. I can't count the number of times the corkscrew has been used to open a bottle of vino for a picnic lunch. The tweezers have pulled out many a cactus thorn from my legs. The list is endless.
A relatively recent addition to my travel gear is a Buff. Recent as in the last 10 years. Far more than a scarf or a hat, it weighs next to nothing and takes up almost no space. For those not familiar with a Buff, look here: https://www.youtube.com/watch?v=sSvRm4CHmvE
Do you have any item of travel gear that you 'never leave home without'?