There is no closed list of types of indemnities. Generally, indemnities can cover claims that third parties may institute (so-called third-party indemnities) and cover any losses that the Indemnified Party may suffer from a breach of the Agreement by the other Party (so-called inter-party indemnities).
The indemnities you would typically want to include in your contract will depend on the transaction you are concluding, the associated risks, and, in some way, your industry.
Common indemnities include:
Indemnities against third-party infringement claims If you buy Software from someone or resell Software for someone, you don’t want to be exposed to any intellectual property infringement claims relating to the product. The Provider usually carries this risk, and the way you transfer this risk to the Provider is by inserting an indemnity against third party intellectual property claims in the Agreement.
Indemnities against third-party claims You can consider including an indemnity in respect of any possible third party claim (it all depends on the risks the Indemnified Party faces). Typically, third party indemnities are provided to protect the Indemnified Party against claims relating to personal injury, damage to property, breach of laws and employee and contractor compensation.
Indemnities relating to breach of contract There are arguments that including an indemnity for the breach of contract provides some substantive and procedural advantages for recovering losses.
There may be jurisdictions where this is the case (provided that the indemnity is correctly drafted).
At the end of the day, if the Parties intend losses can be recovered under the indemnity that is otherwise considered remote, clearly stipulate this in your indemnity!
Indemnities relating to breach of warranties There may be advantages to “upgrading” the warranties to indemnities. If this will hold any benefit will again depend on the wording of the indemnity, what it says about the remoteness of losses and interpretation.