Getting someone fired
There is a guy at work that really really needs to go! I know is sounds terrible and before you say I shouldn't do it know that I have thought about this long and hard and he really needs to go. He would never quit on his own, so I really need to get him fired! What would be the best way to accomplish this? Spam his email with porn? Write a letter to HR?
I know how frustrating this can be, especially when their incompetence affects you, but unless you're the boss it'll be hard to do! If you try to get them fired you may be risking your own job. Maybe speak to someone in hr/leadership etc about how the person in question is affecting your job and how you're worried about productivity dropping.
Alternatively you could try to help them as much as you can?! (I know you've probably already tried this!)
First and foremost, your responsibility is to go through the right channels to voice your concerns about this guy. HR departments are there for a reason and if you go the right way about it, whether you're successful or not, you will know that you have done the right thing. You need backup from fellow workers (written and verbal) when going through HR but if it's personal between you and this guy, then HR could force you both into mediation or even fire you both depending on your workplace circumstances. By being underhand about it and spamming his email, and HR get to hear about it, they will have no choice but to fire you because you are being deceptive about it...and you risk HR wrath by taking matters into your own hands and not trusting them to sort the issue in the first instance which, by the way, is part of their job description.
If you have a boss/supervisor above you, then you really should be taking your concerns to them to start the process to remove this guy and if you feel they won't do anything positive about it, then you may need to consider working elsewhere.