Romania is generally a very safe country to travel in. You can drink the water, there are no civil wars and the most dangerous creature is the drunk Romanian male.
When it comes to driving though, Romania leads Europe in road deaths with terrible roads and drivers out of their minds on drink. Pedestrians in general are regarded more as targets than obstacles to avoid so look both ways and start running.
Also don’t forget that the average backpacker stands out in Romania and as all foreigners are associated with wealth, you’ll be top of the target list of the local thieves. They tend to work in gangs and will distract your attention at railway stations and in crowds, while another rifles through your pockets or shoulder bag. Keep your valuables close to you in public.