Reduce, reuse, recycle doesn't just apply to aluminium cans and other recyclables, it can also be applied to online endeavours. Instead of creating a domain name and eventually subjecting it to the theoretical landfill of the domain registrar because you forgot to renew your hosting or lost interest in your project, consider digging through the landfill to find an unexpected diamond in the rough that suits your idea perfectly.
SEO
Expired domains also have the added benefit of already being indexed by Google, giving you instant SEO benefits for free before you even attach your idea to the domain. Backlinks (links from other websites to your domain) also increase the credibility and trustworthiness of your site to Google, often increasing your page rank results in return.
Catchy
An expired domain could also present a memorable or catchy domain name that you hadn't considered or thought wasn't available.
There are the pros, now for the cons
Cost
Expired domains can cost a lot of money depending on the domain you're looking for, bidding wars can erupt on desirable names with some domains selling for thousands or even hundreds of thousands of dollars. You also need to be aware of the cost of the domain extension, .com domains are usually the most desirable extensions and cost around $20 AUD to register for a year, emerging extensions like .ai can cost over $150 AUD per year to register.
Backlink quality
The quality of backlinks can also be a factor affecting the existing SEO of the domain, backlinks from higher profile websites are more valuable than backlinks from random lower profile websites.
Legal and copyright
An expired domain could also be a potential legal or copyright issue. Some corporations register common mispellings of their brand name, these can occasionally appear on expired domain lists and you may be asked to give it back to them by legal action.
As a blanket rule, stay away from hyphenated domain names, these can often be known brand names or common misspellings that, although they are technically different domains, may get you into legal trouble with the owner of the known brand domain.
Of course, you might not find a domain that suits your idea or website, and that's okay. It's ultimately what suits your needs the best.