Yes, it is possible to take a Cambodian or Vietnamese registered bike into Thailand – but it is not easy.
First you will need all the correct registration papers, and bike insurance. Officially you need the bike to be completely registered in your name, although there are ways around this. If you do manage to take a motorbike into Thailand, you are often given a form stating that you have 30 days to exit, and you have to nominate which border you will exit at.
Our friend Seb found a ‘Power Of Attorney’ form online and had the previous owners of his bike and a Cambodian man co-sign them. Seb crossed the border first, leaving his friend with the bikes. Seb purchased the mandatory motorbike insurance and showed enough authorities the forms that they eventually let his friend cross the border. This took 3 hours.
UPDATE
This comes from Olli and Wooki, two Germans who crossed from Laos into Thailand:
Yesterday we crossed from Laos to Thailand over the Friendship Bridge No. 4 between Huay Xay and Chiang Khong. All it cost us was one USD for some Photocopies, got 30 days in Thailand for free. First, they wanted us to pay for the police car escorting us while crossing the bridge, but when we told them we dont want to pay we didn’t have to.
Finishing the paperwork took about one hour. On the papers it says that we have to bring the Bikes out of the country again, so it seems that we cant leave without them.