*** Improved by Wrobinson on 2/1/2008 ***
The top-level or root domain contains the schema master and domain naming master FSMO roles by default. Depending on the nature of the failure, it may impact your ability to update the schema which is required to install some applications such as Exchange Server, or add and remove domains.
For more information on FSMO roles, review the following MSKB article http://support.microsoft.com/kb/197132
Depending on how your DNS is setup, like Mrdenny mentioned, it may cause some name resolution and replication issues.
*** End Update ***
The lower level domains will still continue to function, however they may not be able to talk to each other.