Although I've been a member here for a while, I never seen an answer to my question... it is possibly very basic and the answer is obvious... but I would still like to have a definitive one.

When flying internationally with stops, can I (and is it desirable) book the separate segments on different carriers on my own and still get luggage checked all the way to my destination?? if so, what are the pros and cons?? would it be more expensive?? I use agents few times before it is almost always not worth it and I had less than ideal experience ... booking on my own online was always a breez but there are some destinations that I cannot make with one booking on my preferred airlines.

I appreciate all input.... details also appreciated since I'm not much of an expert as most people on this forum.