Sakes alive! The people telling you not to travel in Vietnam/Cambodia/Laos are reeeeally out of line. I currently live in Vietnam and have traveled solo in all of the countries you have mentioned. And I'm still very much alive! You should see some of the completely brainless idiots that travel in these countries and make it out alive, or completely unaware of any danger they may have faced, if any. I mean, seriously!! Some people may have had bad experiences but to tell anyone NOT to go because they'll never see their friends/family again? That's just insane.
You can get a visa from Vietnam to Cambodia on the border. In fact, if you pick up a bus ticket through one of the travel companies in Saigon's backpacker district you really just have to pay $25 and the bus driver will take care of it all. You just have to get off the bus to go through customs. You can also get to Cambodia via the Mekong Delta- usually involving a three day tour and then a boat trip to Phnom Penh, if I'm remembering correctly.The road conditions in Cambo have improved in recent years and you can get from Phnom Penh to Siem Reap in about 6 hours for $6-10 depending on whether or not the bus has a toilet. There is a boat between the two cities but no one who knows what they're doing actually uses it. It's more expensive and uncomfortable (no one I've talked to has anything good to say about it). It was only popular when the roads were bad.
The situation with visas for Laos keeps changing so it is advisable to get a visa from an embassy beforehand if you really want to play it safe. I got mine in one day in Bangkok and had no problems. If you get your visa while in Cambodia do it while you're in Phnom Penh! Because wherever you apply from they'll have to send your passport to Phnom Pneh anyway. Travel in Laos is definitely a lot slower than in Vietnam and Cambodia. The road conditions aren't as good and transportation is generally not as reliable, but it's still okay. In Laos I traveled by bus from Vientiane to Vang Vieng, to Luang Prabang, to Phonsavan. Each stretch was between 8-12 hours long and not the most comfortable experience ever but I definitely do not regret it!!
Traveling in Vietnam can go both ways. The whole Hanoi - Halong Bay thing can be annoying but not unbearable (a lot of really disorganized tours, etc.) Hanoi to Sapa involves an overnight train that was a bit sketchy but if you've got a good sense of humor (and a sleep sheet!) you should be fine. Travel in the North is more annoying than anywhere else in the country because there are a lot more scams running. ESPECIALLY traveling to Halong Bay from Hanoi, but it's still worth it. You can buy an open-bus ticket for about $22 (depending on the time of year. don't try it over Tet if you have time/money constraints!!) which can get you (for example) from Hanoi to Hue, to Hoi An, to Nha Trang, to Mui Ne, to Saigon, stopping wherever you wish. There are pros and cons to the Open-Bus system but it's very worth considering.
As far as safety is concerned, just keep your wits about you and you should be in good shape.
Peace!