It depends. Note that in all these examples, I'm assuming the employer has explicitly required you to travel, as opposed to (say) you choosing to live far away from the office and commuting, and that they're already picking up the tab for actual expenses (flights, hotels, taxis etc).
So. If you're a salaried employee, and you travel during working hours, you're already getting paid and there's nothing to charge for. And since salaried jobs tend to entail flexibility both ways, you're unlikely to qualify for overtime just because you had to get up early to go to the airport, arrive a bit late, etc.
However, if you're a salaried employee and you travel significantly outside working hours (late at night, weekends etc), you may be eligible for overtime pay or time off in lieu, because the time you use to travel is time away from your free time. However, this will depend on company travel policy. If you're on a multi-week assignment, many companies will also offer you a choice between flights back home or extending your hotel for the weekend, but they won't pay you overtime unless you're actually working on the weekend.
If you're an hourly employee and you are required to travel, you should be paid for every hour of travel, full stop.
If you're a freelancer or consultant, you can agree whatever you want with your clients and charge what the market will bear, and more often than not, travel time is paid for. In my own case, I charged my regular hourly rate for international travel, computed using the shortest direct flight time. This both compensated me for time when I could not meaningfully work for any other clients and was a nice little earner when I was commuting regularly between Singapore and Saudi Arabia, a good 12 hours apart (no direct flights at the time) -- and the client was OK with this, because there weren't many other people who had both the skills and the willingness to do it.
That said, I've never heard of anybody claiming compensation for packing their bags -- just how slow a packer are you? Even the most generous travel compensation is usually measured from the door of your home to the door of the client site.