Why do we hear everyday about people getting prosecuted because of comments they made on twitter but not on Facebook or reddit?
I know very little about social media but it's not that difficult to hide your identity online unless NSA is after you for terrorism.
It's not about your anonymity, but about your audience. As @darkf mentioned, Twitter doesn't have the same level of privacy settings that Facebook does. A user's tweets are either all protected or all public. This means that you have less control over your audience. A message that you meant as a sarcastic comment could be retweeted (repeated with attribution) by a friend who thinks it is funny, but someone you don't know could miss the sarcasm and interpret it as a terroristic threat and report it to the authorities. At this point, because of the public nature of Twitter, the authorities do not need a warrant or a subpoena to view your statement; depending on the level of personal detail in your profile, they might not even need Twitter's cooperation to identify you directly.
Facebook's privacy settings are really not any protection against law enforcement, since Facebook will comply with legal requests to access your content. Its real "benefit" in this situation is your ability to control your audience: if only your friends see your sarcastic statement, it is much less likely that they will turn you in to the authorities for making terroristic threats, since they are more likely to understand your tone and the unlikelihood that you are seriously making a threat.
I didn't address Reddit. Because a large part of its structure is as a link aggregator, the opinions and statements of its users are primarily found in the comments, a lower-status area that doesn't get as much attention for a few reasons:
In other words, the signal-to-noise ratio is too high to make monitoring Reddit (or taking threats there seriously) of much worth to law enforcement. Twitter is really in the sweet spot between strong identity links (people using their real names and investing in their account's status) and openness of content to observation. Twitter's API even makes it easy to monitor for threats: you could have a feed consisting solely of tweets using the word "bomb" that originate in Birmingham, for instance.
bonsaivikings answer does make sense for Twitter and Facebook, but Reddit doesn't really fit in there. It's not just about the audience - it's about how the audience perceives you. Anonymity has great influence on the general behavior of the whole community, which affects that perception.
Users on Reddit are mostly anonymous and almost every post is public with a large and diverse audience (at least in the main sub forums). A user's post history could be used to identify him if he's careless about what he posts. Signup is easy and does not require email verification though, so "throwaway accounts" are commonly used to post thing that should not be linked to the main account, like provocative posts, incriminating confessions or embarrassing stories - all popular subjects on reddit. On the other hand, the reputation system gives users incentive to write about those popular subjects on their main account, to gather upvotes.
Because of the anonymity and/or the reputation system, many stories are completely fabricated. "Everybody lies". Popular posts get questioned and users often demand proof when other users make any claims. Other user see those posts as entertainment and don't really care whether a post was sarcastic, a lie or the truth, as long as it is interesting. Any "threats" like we see on Twitter would be deemed as uninteresting and usually get ignored or downvoted, so those post don't get much exposure. A user who is posting a threat or something self-incriminating would have to provide proof before he is taken serious by the community. That usually doesn't happen.
Twitter is publicly visible. On Facebook, your posts can be seen only by whomever you've set in your privacy settings.
As for Reddit, I can only suggest anecdotally that more people talk about their real life, and add real life acquaintances, on Twitter. Reddit is a bit more detached.
