There's a lot of possibilities. First, make sure that you have the latest copy of the DoomBuilder files. They've been updated many times recently.
http://amuletsandarmor.com/download.htmSecondly, make sure that you have all 5 files that go with the new map. You need:
L##.MAP
L##.GEN
L##.I
L##.LIT
S##.SRP
Note that one of these files begins with an S, not an L. This was an issue that took me a while to figure out and caused crashes after loading.Thirdly, make sure that you did not copy the wrong script file. The one in the TemplateMap folder that comes with the doom builder files is an empty script file, this is what should be used with most levels unless you've started making custom scripts.
Fourthly, make sure that no linedefs or sectors have any actions. Actions try to call scripts and if they don't exist at level load, the game will crash. Traps, platforms, and all other moving objects do not work like they do in doom. Except for doors which use alter sector things, all moving objects require scripting which is triggered based on action numbers.
Fifthly, back up your map and then delete all of the THINGS in the map. Then add a player 1 start. This will let you know if you have either a bad thing number OR an alter sector thing in weird geometry.
(Strangely enough, having too many alter sector things within nearby sectors can cause issues. Also if your sectors are concave, certain alter sectors don't always work right. You can fix this issue by turning one strange shaped sector into many sectors with linedefs.)Lastly, check all of your sectors and make sure that they are not still a part of another cut sector. Sometimes if you try to draw a new sector in between a larger sector, the two halves of the larger sector remain with the same number. The most common way to achieve this is while making doors. Sometimes two sectors don't split properly. Use the Create Sector tool to split them up if this is the case anywhere. I actually had a crash during load because of it at one point as well.
Another helpful thing is to check the error.log to see what crashed. Post that here and we can hopefully provide some more info.