There are multiple Baby Tycoon downloads. They have the LCID problem that Yellowrose mentions. So they will cause a problem for people with a Zoo Tycoon version that is not using American English or one of the other languages they are configured for. However, that problem would cause a crash in the purchase menu and not elsewhere. They have other problems as well. But I do not believe those other problems would cause a crash. The Tree House also has problems. But, again, I do not believe its problems would cause a crash. Except for the freeform unlock, I do not use other hacks on a regular basis. So I cannot speak on them.
There is a limit on how many user creations may be added to the game. This limit is 3000 or a little over. I suspect you did not hit that limit.
You might want to check your ".dll" files. It is known that user ".dll" files that changed or copied lang0.dll will cause sporadic crashes. If you have any user ".dll" file in your Zoo Tycoon folder that is larger than 1.8 mb, delete it. If you have any ".dll" file with "backup" in its name, delete it. Compare the size of lang0.dll on your harddisk with the lang0.dll on the Zoo Tycoon CD-ROM. If they are not the same size, copy the one from the Zoo Tycoon CD-ROM to the harddisk.
There could also be problems with some other user created animal that you have. Some of them can be difficult to find. For example, maybe they only cause a crash when they try to swim or try to escape or try to do some other activitity that they do not do very often.