Using the downloader is definitely a breach of YouTube's terms of service:
"You may access User Submissions for your information and personal use solely as intended through the provided functionality of the YouTube Website. You shall not copy or download any User Submission unless you see a 'download' or similar link displayed by YouTube on the YouTube Website for that User Submission."
You could argue that agreeing to the TOS is the equivalent of entering into a contract, if YouTube could prove a financial loss due to your breach of that contract they could take legal action to recover any losses plus costs.
In addition, if the copyright of the content you download is owned by someone else (and you won't be far wrong if you presume that all of it is copyright material) and the owner doesn't give you explicit permission to download that content you'd be in breach of copyright laws.
Ft. Lauderdale, Fl USA
So it is illegal? But obviously not illegal enough to deter people, or rather so loosely, that converters like the above can basically invite people and openly give them a service that enables them to download almost any song for free from youtube. It may also be safer than paying for music on the internet since you don't need to share personal information (such as your credit card number) for the "transaction".
[This message has been edited by Essorant (01-17-2012 11:07 AM).]
The software itself is legal, what you do with it is potentially illegal especially if you're using it to download i-tunes content without paying for it.
The only grey area concerns the people that wrote the software who, without actually using the software to commit an illegal act themselves, could still be held responsible for any illegal act committed using the software. It all depends on intent - if the software has an obvious legitimate use and only accidentally allows you to use it to commit an offence they might get away with it. If the only use is to commit an illegal act they're likely to be on shaky ground - especially if they're openly advertising the illegal part as a feature.