This varies from system to system (e.g. list of task fields supported for Redmine bug tracker is different
from the one for Microsoft Project or JIRA). These are the basic task fields supported for most systems:
Task Start Date
Time estimate (hours)
Task Type (bug, feature, task, etc)
Task Status (new, assigned, in progress, closed, etc.)
Task Due Date ("finish date" or "estimated finish date")
Priority (High, Normal, Low, etc).
Assignee name (can require admin permissions for some systems)
Relations between tasks (e.g. "task 1 precedes task 2") - this is currently supported for Redmine and Microsoft Project only.