A DoS (short for "denial of service") attack is a form of attack used on web services which aims to "crash" the service.

Is there any motive of this form of attack besides crashing the service / website?

For example, I could think of blackmailing/ doing harm to a competitor / political reasons as a direct motive for DoS attack. But are there other, more indirect motives? Would it be possible to get data from the service with a DoS attack? If so, how?

In general a (Distributed) Denial of Service attack will not provide you with much information directly. However, there are a few scenarios where information could be gleaned as a result of a DoS. The following are a few examples, but this is not at all exhaustive:


A load balancer may divulge internal subnet information or leak internal machine names in situations where backing systems are offline.
A DoS that shuts down the database first may cause an application reveal the database engine type, connection username, or internal IP address via an error message.
A poorly implemented API could result in a "fail-open" scenario--DoS'ing a Single Sign On server may give an attacker the ability to log in unauthenticated, or with local credentials.
In Advanced Persistent Threat scenarios, DoS'ing detection infrastructure may allow an attacker to remain undetected during other information-gathering stages.
Similarly, DoS'ing the admin interface of a firewall could hinder network administration's incident response efforts.
In an extreme case, DoS against a key-revocation service could allow an attacker to continue to use revoked, or known-compromised credentials.


Other motives for a Denial of Service attack become apparent if you consider the users of a system as targets in addition to the system itself: A Denial of Service attack against a website that sells concert tickets may allow an attacker to buy tickets to a event that would have otherwise sold out in minutes. A DoS against a version control system could prevent a development company from delivering software on time. A DoS against a social media site could make coordinating political protests more difficult, or event impossible. 
