The reason that scammers try to get ahold of your information is pretty simple. It's almost always about money. Sometimes it takes a bit more of a roundabout form.
Phishing for banking or credit card information is pretty simple to understand. If a dishonest person gets your sensitive personal information, then they have a lot of options for normal theft or different forms of identity theft. Naturally, this information is in hot demand. Online banking and online shopping open up tons of possibilities for making easy money with stolen information. You should be incredibly suspicious of anything that is asking for your banking information.
Note that Paypal and Ebay, in particular, seem to be targeted often. This is probably because money stolen from a paypal account can be withdrawn to a foreign country through a dummy account very quickly. If done properly, then it will be impossible to retrieve it. Paypal phishing scams are extensive enough to warrant their own article.
Of course, they don't just try to get your banking information. Sometimes scammers are more creative. If there's a chance to earn money doing something, someone will eventually figure it out. For example, phishing scams exist that try to steal online accounts. Steam Accounts, Xbox Live Accounts and World of Warcraft accounts have all been targeted through standard phishing scams. In these efforts, someone usually claims to represent the support team for the game. They then cite a problem with the account and get the person to hand over their login information. With a few clicks, the victim is locked out of his account and the phisher has his prize (which could usually be sold for a fair sum of money). More inventive scammers would target people who were selling their own accounts on online marketplaces. Since this technically violates the terms of service for the account, phishing emails would claim that the relevant service would permanently kill the account unless they gave them the necessary information in an "amnesty program." This turned out as you would expect.
The point you should take away from this is that phishing scams are constantly changing to take advantage of new markets. They will do whatever they can to separate people from their money. Find out how to protect yourself on the next page.