Yes you can travel with furniture and other household goods in a van. That's what vans are made for. :)
Three things you should consider:
1. Customs Unions
No need to declare anything when crossing borders between countries that are part of a customs union. In Europe for example you have Switzerland that is inside Schengen but not inside the EU customs union. Hence you'll have to go through customs checks to drive through it with a loaded van. These include providing a detail of the contents of the van, demonstrating that the goods are not for sale and have no commercial value, and paying whatever custom duties are involved upon entry, to be reimbursed when exiting the country. See the image below (courtesy of Wikipedia) for the map of the countries inside the EU customs union:
2. Vehicle Limitations and Road Safety
You must respect the maximum gross weight limit for the vehicle you use, as well as the allowed extra dimension for goods longer than your vehicle if applicable. This is an issue both for road safety: routine police checks can take you to places where you weigh the van and its contents to check for this, as well as for customs since any country with customs check will weigh a loaded van. Again this is the case for Switzerland to name one.
3. Proof of Ownership
Ensure you have proof of ownership of some sort. A letter signed by your friend translated in several languages, along with a photocopy of their valid ID will do. This is just an extra safety measure you take to avoid being accused of robbing someone's house. Of course you could always say the stuff is yours, and it might probably be hard for police officers to demonstrate otherwise. Moreover so long as nobody reports a van full of stolen goods nobody would have a reason to suspect you. Nevertheless the main objective should be to get from A to B as efficiently as possible. Being held up by zealous police officers in a foreign country is something that will most definitely spoil your journey, let alone cause you delays.
All in all the European Union customs union have made these matters a lot simpler than they used to be a while back. As long as you stick to such countries there a big chance you'll never encounter a single content check on your way to wherever it is you are going. This is of course assuming that you are a cautions law-abiding driver.