Here is an exciting list of projects which plan to take advantage of sidechain technology.
1. Bitcoin Extended
A heavier, less decentralized chain for higher-throughput, cheaper Bitcoin transactions. Aims for simplicity and modularity; Bitcoin Core + BIP 101.
P2P Oracle System and Digital Marketplace. This project aims to revolutionize the way information is created and diffuses through society. As a side-effect, it creates efficiencies in capital markets, destroys scams, and creates certain types of digital insurance markets.
Forged in the Chamber of Secrets by the Dark Lord himself, this hyper-specialized transaction system is far less programmable than Bitcoin, but features a 'magically' shrinking blockchain.
Blockstream's exchange-centric project, supporting: digital asset issuance, confidential transactions/confidential assets, and rapid confirmations.
A reimplementation of Ethereum, led by Bitcoin veteran and world-class security researcher Sergio Demian Learner. Has less self-deception than Ethereum, and less dream-selling, but has more "actual work" and professional ethics.
6. The Elements Project
Blockstream's Labratory. Where extremely technical (and highly ambitious) features are tested before they make their way to Bitcoin Core.
A P2P Dropbox. Matches users who want to back up files, to users with unused hard drive space. Sortof an "AirBnB" of hard drive space.
8. Bitcoin Codex
A re-design of Namecoin as a sidechain. Has the potential to greately improve internet safety, privacy, and reliability.
These are great projects, whose codebase we might use as a sidechain of Bitcoin.
Uses ring signatures for greater transaction privacy, at the chain level.
This project uses zk-snarks for extreme privacy. In fact it's so private that no one really understands what's going on in here.
11. Original Ripple
Original Ripple allowed users to extend credit to their friends, and for that credit to then be extended to friends-of-friends in a big trust network.
A P2P message system emphasizing privacy. With BTC fees, we might have a solution to the problem of e-mail spam. We could then break Google's hold over our entire communications infrastructure (and password-reset infrastructure). Perhaps even LinkedIn and even Facebook would end up disrupted.
Edit: I think this particular use would not require drivechain per se.
Digital asset market, with P2P trades. These assets are usually for games, or collectables, but they may also be backed by TTPs to enable ‘stocks on the blockchain’, 'gold on the blockchain', 'airline miles'.
Physical contraband market. Currently the production version uses Bitcoin Testnet for messages. A sidechain might be more stable, and might allow for the system to automatically confirm that BTC payments have taken place.