Originally Posted by beachmouse

Many airlines will have agreements with other carriers to interline baggage so you can check it all the way through. Inquire with the airlines you're interested in using to see if it applies to them.

The problem comes if you have a delay with your first flight that would lead you to missing your second flight- unlike booking a single ticket where the airline has to get you to your final destination at no additional flight charge, the two ticket approach means that if you no-show for your second flight, the ticket will almost always be cancelled and you'll have to rebuy another ticket to your destination at a much higher last minute price.

So if you feel like the risk is worth it, give yourself a huge, huge layover.