It's not entirely clear to me whether you're referring to asset fields or ticket fields.
- Asset fields cannot be deleted from the database, though you can clear their contents. You can rename the fields under Configuration\Asset Pages. To clear a field for all assets, click the Assets link at the top of the console, tick the upper checkbox, hit the Mass Change button on the left, select the appropriate field and insert a blank value into the available input box.
- Ticket fields can be removed under Configuration\Ticket Content, section Ticket Custom Fields.