Can a worm, trojan, virus, spyware, etc. stay with your computer if you do an entire reformat with recreated partitions? Delete then format?

If you are talking about zeroing the drive (also called a low-level format) - writing zeros to every sector of the drive, then no.

There are boot sector viruses that are harder to get rid of. There are also programs like C-dilla (DRM) which install stuff to a small hidden partition. Zeroing the drive should kill all.

Are you speaking theoretically? If you need help removing something specific, let us know.

Welcome to SAF :

ok, format = no, fdisk = no

One might luck up with some viruses using the above BUT why use Fdisk, Fdisk/mbr or format to remove a virus when there is free anti-virus software that will safely do the job?
Even a image backup that blows out the partitions to re-install isn't total protection........ but I will say, dang good thing to have :-)

AV programs use BIOS calls to access the hard drive, and remove the virus nasties because they could be in many places and some infect with double executables to serve up another disk of nasties when you think you have it cleaned up.

Bottom line, check in with your AV supplier for a tool...