I hope this link will help you in your search as much as it helped me. Bear in expect mind that some of the companies are defunct or don't have up to date phone/fax info, however it is a start. As some of the guys in this forum have said there are quite a few job placement companies that interview hire and train pilots for different companies. This primarily works for guys/gals that are current/qualified in the aircraft they expect to fly. So if you have 737 experience and the company has 737's they'd interview you and train you for the company. Most of the time your contract doesn't allow for an upgrade, you have to double check.
That being said, you sound like you're interested in doing some real seat of the pants flying. The link below should be enough to get you started. You can click on countries all over the world and find operators, equipment and most importantly addresses and contact info. Just expand your search when you find a company you like and do a little research and background info on them. Good Luck!!!!
Here's the link:
www.pilotcareercentre.com/