Is there a bus or train that goes from Bangkok to Ho Chi Minh City?

Going overland you got several choices. I have actually done the trip and it can easily be done in 1 week but a bit tight on the start/ end cities. 10 days would be great. Example- Land late in BKK (most flights from overseas are late night arrivals & by the time you clear the madhouse of immigration and customs you must navigate to the taxi ranks. If you do arrive during normal operating hours there is a skytrain to take into Bangkok proper. From there you can easily grab a taxi to Koh San Rd area where the cheapest tourist hostels are located along with increasingly upscale mini-hotels with inflated prices. But this is the center of the action so to speak so many if not most of the first timers stay in the immediate area around Koh San Rd. Just be careful on the typical scams.

Spend 2 to 3 days in Bangkok and you will still have not seen the tip of the pad thai-berg. Anyways you can grab a bus for something like $25-$30 USD. Book carefully and check prices. Try to make sure you get a real ticket. Some places which tuk-tuks take you to are just there to scam tourists. Don't ask any tuk-tuk or taxi driver to recommend someplace, they will take you to get ripped off so they get a nice commission or kickback for it. Train tickets sold at mark-ups of 10 or even 15 times over real face value etc.

I suggest a day bus from Bangkok either Koh San Rd or Mo Chit bus station which is easily reached by the MRT skytrain for cheap. You should arrive in Siem Riep in one piece but a bit tired and overheated, depends. Some bus staff have been known to drive a hard bargain to scam gullible tourists. Best to avoid the buses leaving from Koh San Rd and head to Mo Chit for a real Thai bus which is government run so it is safer and better.

Next up is the run to Siem Reap, crossing the border, getting the Cambodian visa which usually results in some attempts at extra cash donations. You can give $ 5 extra or argue with the Cambodia immigration agents... Don't be surprised to get called last for your visa if you failed to hand over the fiver.

Next the bus will drop you on the side of the road and the tuk-tuks will jump you, and even if the bus company says the tuk-tuk is free, it isn't. The driver will try to pressure sale you into a trip to Angor Wat. Choice is yours. But if you decline please cough up at least $2 bucks better $3. Next you will want to go to Siem Reap which is hot as hell. $20 USD for a day ticket and on a 7 day trip that is all you will have. Even on ten days you would be lucky to spend 2 full days in SR. Next you need to take a bus to Phnom Penh. No reservation needed just tell your guesthouse the day before. I think every guesthouse in SR provides these services. You pay them direct. Keep some smaller bills like single USD notes for tipping. After you arrive in PP you have 2 choices - overnight it or get on a bus for the 7 hour trip to HCMC, VN. Provided you already have a visa for Vietnam because there is NO visa on arrival VOA service at any land crossings, only at the major international airports.

I would probably spend the night in PP and have a few beers. But be careful! PP is the wild west of SE Asia :-D

Once you arrive in HCMC the bus should drop you off in the backpackers mecca of Pham Ngu Lao and bordered by Bui Vien street. All the cheap beer, eats & hostels/hotels etc are there and dedicated to dealing with foreigners.

Same idea with the first comment. There is no directly train or bus from Bangkok to HMCM. You have to pass through Siep Reap and Phnom Penh then HCMC. You can refer the route at: Wikitravel. I think that,you can book tour travel around Thailand-Cambodia-Vietnam sounds good. Further, about 7 days, you can visit Ho Chi Minh City - Mekong Delta - Hoi An. In Mekong Delta, you can homestay at local people and join the floating market in early morning. Last year, i visited Mekong Delta in 2 days, it's wonderful tour with me. Happy travel