The easiest way to stop your boss from getting trivial emails is to stop encouraging trivial emails.
At my work, we use Outlook and Lync. Generally, we reserve banter for Lync and use email for things that we feel there should be a record of (since Lync does not and can not reliably record conversations. Don't get me started.)
I wouldn't explicitly discourage a joking email, but I certainly wouldn't send them unless you didn't care if they ended up in your boss's inbox. I personally make a lot of jokes, almost to the point where people wonder if there's something wrong if I don't make one. But I don't ever put anything (joke, insult, opinion or otherwise) in an email. Whether I think it's going to end up in my boss's inbox, or his boss's or the senior director's or the CIO or the CFO or the CEO, or the intern a few cubicles over. I just wouldn't put it in an email ever.
Now, there's a difference between trivial emails and joking/embarrassing emails. If the email is something like "Joe, we decided to go with four pixel borders on the widget." and it ends up in your boss's inbox, that's bad. That is probably a very small detail that your boss doesn't need to know. (Okay, maybe there was a big political battle over borders, I've seen stranger things, but generally that's a small detail your boss doesn't need to know about.)
If people are clogging up his inbox with crap like that, there's one of two possibilities. 1) They don't know any better. In this case it's your boss, not you, who needs to speak up if he doesn't want these emails. The other possibility is 2) They need to CC your boss on everything because they perceive you (correctly or not) as a non-deliverer. If this is the case, you need to remedy that immediately. If it's true, then you need to start delivering so they don't feel the need to have your boss included on everything. If it's not true, you need to find out why they feel that way and clear up the situation.
tl;dr - Don't do embarrassing things. Don't worry about your boss's inbox. Do get work done.