Indexes not defragmenting

I have been given ownership of this 2005 database with a large number of tables. Speed has been a problem so I looked at % defragmentation on the indexes and found that most were over 50%, some as high as 98%. I rebuilt the indexes using a script I wrote but some refuse to reduce their level of defragmentation even after I dropped then and recreated them individually.
Any ideas how to get around this?

Thanks, good read though a bit more on why some don't defragment would be good.
Yes, I do have some heaps, not many though and I now understand that these are stored in non-contiguous blocks and therefore do not defragment. Is that right or is theresomething else to it.