are you sure you are dragging the proper file? i mean, if you're downloading applicatins they are likely to come either as a .dmg file or a .sit-file. depending on what you got you do the following;
if your download appears as a disc on your desktop, open the disc-image in finder and then drag the application(mostly the one file named whatever you downloaded) to your application-folder.
if your download appears as a .sit-file you have to unpack/unzip(to use windows words) the file before you can use it. use StuffIt Expander (applications->utilities->stuffit expander, or just dobbleclick) to do so. then you'll have the raw files of whatever you downloaded and you may drag the application to your application-folder or other desired location..
note that some disk-images may come as a .sit-file to begin with. this means you might have to do both steps, unpacking the .sit-file and then open the disk-image in finder to view its contents, and then drag the application-file to its folder..
afterwards you're free to delete whatever the application came as originally. just drag it into the trash and the .sit-file will be deleted and the disc-image unmounted/ejected..
hope it helps!
alex.