The study of fallacies is most certainly useful because it can help us understand the ways in which others are trying to persuade us.
In times of political elections, we hear various candidates using all sorts of arguments to get themselves elected. One of the most common is the ad hominem attack, in which they attack the person rather than the person's ideas.
We frequently hear "slippery slope" arguments made regarding topics such as stem cell research, same-sex marriage, or other controversial topics. Advocates on either side of the argument will claim that horrific consequences will occur if one course of action or another is taken.
The study of fallacies also helps us recognize the way that advertisers are trying to manipulate us. Marketers frequently use a "bandwagon appeal" to try to get us to buy a certain product just because everyone else is doing it.
One final reason why we should study fallacies is so that we can recognize them in our own writing and speaking. We need to take great care not to use fallacies in our own words. Our logic needs to be as sound as possible.