Here is some information about dogs hitchhiking with humans and humans hitchhiking with dogs. A couple consisting of a dog and a human isn't necessarily hitchhiking slower than a human couple.
Drivers' reactions, though, are more definitive: either a strict "No, never!", or very passionate "YES!". People who like dogs do not hesitate - they just stop. Even when otherwise they won't be picking up a human hitchhiker traveling without animal companion.
Some religions say that dogs are dirty, some countries ban certain breeds, and in some cultures dogs aren't pets but livestock. Take into consideration these cultural differences and learn about animal issues in particular location before hitting the road and crossing borders.
Most countries have laws about what is required from you to enter with a pet. If you check these in advance, you can make the necessary arrangements and avoid quarantine in most cases. Since January 2012, the EU's laws made it easier to travel within the EU as long as you have a valid EU Pet Passport. But even then it's important to check each country's rules in advance - some of them have extra requirements like tick, flea or tapeworm treatment (e.g. UK, Ireland, Finland, Malta).
Advice for Humans
- try to make your dog accustomed with hitchhiking when he/she is still young
- make sure your dog is not afraid of cars before you hitch with him/her for the first time
- don't forget your dog's passport and papers
- make sure your dog feels comfortable and safe in every moment of your journey, for example, don't forget he/she also wants to pee after sitting a while in a car ;)
- flea and heartworm preventative is important also
- keep in mind that dogs cannot go as long as humans without water - take more water than you think you will need as you might need to pour it on them if they get too hot.
- putting your dog on a feeding schedule may be difficult on the road but is worth it and helps prevent 'accidents'
- take a towel or an old jumper for your dog to sit / lie on. On hot days this can protect them from hot pavements when you are waiting and it can also protect the car of whoever gives you a lift.
- if hitchhiking in hot weather take some Vaseline to help protect your companions paw's from hot Tarmac (or baby socks, but your companion may not find this dignified) and sun cream if your dog has thin light hair - especially their nose.
- practice lifting your dog above your head, and make sure they are comfortable with this so that you can get them into a lorry quickly and safely.
- if your dog is normally happy to get into a car, and they make it clear that something bothers them about this particular lift, trust their judgement, make an excuse, and wait for another lift.
- make sure your dog isn't too close to the road as gravel may hit them, and their eyes are much nearer the ground than yours, so at higher risk of being hit.
- take tweezers(for ticks), a bandage and if you can get them, some butterfly stitches or staples if you are travelling long distances.
- if your dog is clearly tired and has had enough, call it a day if possible. You are a team!
- add more info? :)
Advices for Dogs
- do not drink too much before traveling
- if your fellow human is somewhat stressed, try to be nice and do not annoy him/her too much
- do not run over the road, this can be dangerous
- always look nicely at the driver
- insist on a ride in a dog's own, specific way:
- do not bark at cyclists and other traffic, it can contribute in worsening of the hitchhiking image
- as humans world is weird and sometimes incomprehensible, listen to your fellow human to be safe
- always be polite to other humans and dogs that are already in a car
- inform your fellow human you are hitchhiking with about your intentions to flirt with a dog that happens to be in the same car
- make sure not to get motion sickness!
- add more info? :)