This post includes a list of ways in which indemnification can benefit a party bringing a claim. Here, in a spirit of completeness, is another one, suggested by a reader:
Ensure Losses Aren’t Covered by a Provision Excluding Certain Types of Damages. Asking to be indemnified for losses incurred due to nonparty claims constitutes a claim under the contract. That would make it difficult for the indemnifying party to argue that those losses constitute consequential damages or some other kind of damages falling within the scope of a provision excluding certain types of damages.