The given answers focus on the open p2p blockchains of Bitcoin and its likes.
There is however also such initiatives as Hyperledger, R3 Corda, and Enterprise Ethereum Alliance, etc. (Even cloud providers (eg aws) have offerings). These kinds of platforms tend to avoid the time-consuming proof-of-work part and do consensus between selected parties, not being open for anyone with an internet connection necessarily. They also do not always display information in the blocks to the entire world; and instead tend to have protections regarding who can read what on the chain.
These platforms tend to promote their usefulness in cases where parties not wanting to trust each-other, or a third party, with some information, still need a shared source of said data, with agreed-upon rules of how the data will be changed that can be verified.
Goals in using such distributed ledgers include different things, such as added security, transparency and auditability, anonymity, scalability, increased industry collaboration, and allowing for new business models. Which, and how, would depend on which industry and application, but maybe some ideas can be found in this survey or similar placessimilar places. These kinds of platform are likely what existing companies would look at using if they got into the blockchain space.
Looking at pieces that the platforms advertise actually being used in, we find such initiatives as:
Commodity tracking
- for example major food producers and retailers joining a network aimed at "...connecting growers, processors, distributors, and retailers through a permissioned, permanent and shared record of food system data.".
Data sharing
- for example insurers sharing data for compliance reasons to a network where regulators with permission can look at it. There can also be improved handling of documents on a network instead of current siloes.
Personal information control
- for example hu-manity.co controlling how personal data is shared with companies.
Since blockchain is new and untested, there would at the moment be more experiments and proof-of-concept applications rather than real-world ones. Many of them will turn out to be poor matches for a hyped technology looking for a problem to solve. However, permissioned or consortium distributed ledgers is one place too look where smaller projects have started to be launched for real applications.