It can be very frustrating when a lot of spam starts to come into your mailbox. Your first port of call should be to enable the SpamAssassin feature within your cPanel control panel. This will give you the option to be able to set the acceptable spam levels per mailbox and what should happen to the mail if it has been marked as spam.
Additionally you have the ability to set up automatic filters at either a mailbox or account level that can route emails on specific criteria. i.e. if you are receiving spam from a certain top level domain you can send all of that email directly to a spam folder.
If you start receiving an increased amount of spam, with junk mail filters enabled, then there might be a problem with the mailbox that your spam emails are usually moved to. You should check that the target mailbox or mail folder isn't full or disabled.
If the level of spam you receive continues to increase, then you should consider being wary of where your email address is given. Many spammers will trawl websites for email addresses in plain-text, to add to their mailing lists.
For this reason, some people do prefer to give their email address as an image on their website, to stop their address from being picked up by these spammers.
Additionally, if you're receiving plenty of bounce-back emails which look like they're from spam, it is plausible that your mailbox has been compromised and is being used to send out spam emails. In this circumstance we'd highly recommend re-setting your mailbox password, and running a full virus scan on your own computer, to make sure there's no trojans intercepting your mailbox login details.