The Weekly Halachic Analysis
While you could have thought that there's nothing to lose by answering amen if you didn't hear the bracha, the gemara seems to shatter such an idea. Shockingly, the Gemara Brachot 47a states that if you didn't hear the bracha, you should not answer an Amen Yetoma, an Amen, which is orphaned and separated from the bracha. Moreover, Ben Azzai says not only is it forbidden, but if you do it, there is a curse that such a person should pass away, leaving his children orphans, Chas VeShalom! What could have possibly prompted Chazal to consider answering Amen Yetoma such a grievous sin?
In order to address our question, perhaps we can gain some insight from seeing how the Rishonim defined the parameters of Amen Yetoma. Rashi and Tosfot ask that the Gemara Sukkah (51b) seems to contradict the Gemara Brachot. The Gemara Sukkah relates how there was such a multitude of people in the shul of Alexandria that some people couldn't hear the Shaliach Tzibbur. To facilitate people answering Amen, the gemara says, the Shaliach Tzibbur would wave a flag as he finished the bracha so everyone could see that they should answer Amen. Seemingly, this gemara takes for granted that it is permitted to answer Amen even if one didn't hear the bracha. Rashi and Tosfot both answer that answering Amen is only an issue if you don't know which bracha was made or if you don't know if someone made a bracha at all. If you know that someone made a certain bracha, however, even if you didn't hear it, you can say Amen. That's why the people of the shul in Alexandria were able to answer Amen even though they didn't hear the bracha.
Based on the explanation of Rashi, one could suggest that the reason that saying Amen without knowing which bracha was made is so severe is because Amen is meant to be a statement affirming the truth of the blessing, expressing one's faith in Hashem's abilities and praise. If you don't know which bracha was made and you still say that you affirm its validity, your words become meaningless. Moreover, your intended praise of Hashem turns out to be hollow and without understanding. That's why, says the Maharal, unlike a bracha which is valid if said without understanding as it is intrinsically meaningful, however, an Amen is a statement of Emunah which is useless without understanding.
Summary of the Daily Halacha's
- There are four common mistakes when responding אמן.
- One must make sure pronounce the kamatz under the Aleph of Amen, otherwise it is considered an Amen Chatufa. Additionally, Amen Chatufa includes when someone responds Amen before the bracha has been completed. 
- One should ensure to pronounce the nun of Amen, otherwise it is considered an Amen Katufa. 
- One should be sure to answer Amen slowly. One's amen should take as long as it would normally take to say El Melech Neeman, but not overly protracted.
- If one didn't hear a bracha, one shouldn't answer Amen, otherwise it would be considered an Amen Yetoma. If one didn't hear the bracha, but knows what bracha/Kaddish is being said, one may in fact answer Amen. However, if one is attempting to fulfill an obligation with someone else's bracha, but did not actually hear the whole bracha, one can answer amen even though he will not fulfill his obligation.
- According to Ashkenazim, one should not respond Amen to one's own bracha. If, after making a bracha on food, one answered Amen to one's own bracha, it is considered a Hefsek. Also, if someone else made the same bracha at the same time that he did, he should not respond Amen because it sounds like he is responding Amen to his own bracha.
- Rashi (Brachot 47a s.v. Yetoma) and Tosfot (Brachot 47a s.v. Amen)
- Regarding the halacha, whether the opinion of Rashi is accepted, see S"A 124:8
- This explanation of Amen Yetoma is developed by Rabbi Zalman Melamed on yeshiva.org.il. Rav Soloveitchik in Reshimot Shiurim (Brachot 47a, p. 501 s.v. VeNirah) explains that Rashi and Tosfot hold that Amen is a function of expressing one's Emunah in the content of the bracha, in which case only knowledge of the bracha is necessary. The Rabbenu Yonah, however, understood that Amen is a way of accepting the bracha upon oneself, in which case, having knowledge of the bracha without hearing its words isn't sufficient.
- Netivot Olam (Netiv HaAvoda ch. 11; Sifrei Maharal Edition v. 1, p. 112)
- S"A 124:8, Biur Halacha 124:8 s.v. Kriyat
- S"A 124:8, Biur Halacha 124:8 s.v. Kriyat
- S"A 124:8, Mishna Brurah 124:36, Brachot 47a
- Mishna Brurah 124:31 and 124:34, S"A 124:8
- S"A 215:1, Mishna Brurah 215:1 and 51:3