Ruse-Giurgiu border crossing
The Ruse-Giurgiu border crossing connects Bulgaria (Ruse) and Romania (Giurgiu). The border is the Danube River, which is traversed by the Friendship Bridge. Walking across the bridge is not permitted as of August 2009. Both Romanian and Bulgarian passport control is done in a single office on the one or the other end of the bridge.
UPDATE August 2016 - Successfully walked across the bridge, border guards confirming it was possible but advising to be careful. Footpath exists on both sides but may be obstructed in parts, meaning you must walk on the road. I advise against doing this if it is dark. Takes 30-40 minutes. Good hitch hiking spot for travellers entering Romania (e.g. going to Bucharest) exists immediately after border control on the Romanian side
South to Turkey
Right after the Bulgarian passport control there is a roundabout. Stand at the roundabout point towards Sofia and Varna with a sign reading TR, or ask truck drivers who briefly park after passport control.
About 15 km down the road there is a Turkish truckers restaurant Haji Baba. It's a much better spot to hitch traffic as Ruse is quite a big city and at the restaurant there is much less local traffic. You can also try to hitch a ride straight to Istanbul (but leave the truck, with all your stuff, before the Kapitan Andreevo-Kapıkule border crossing).