Unluckily, although PGP is awesome in theory, the "real world" benefits of PGP are quite limited, if existent. If PGP was the default that everybody uses, it would rock.
TLS gives you (ignoring the possibility of exploits) a secure connection to your mail server. You have the guarantee that the server you talk to is really your mail server, and that nobody can eavesdrop on your communication with the server. However, there is no end-to-end encryption, nor message authentication.
Which means that although your communication with the server is confidential, your messages are stored in plain text on the server (and forwarded to the NSA anyway, don't be fooled into believing anything different).
Also, the exchange with the recipient's mail server may or may not be secured (you don't know), mail on the receiving (and intermediate) server(s) is stored in plaintext, and the recipient may or may not use a secured connection with his mail server.
Further, despite some extensions that thwart the most trivial spoofs, the protocols used in email exchange are pretty naive and give little to no guarantee about a message's origin. In other words, you do not know with any reasonable certitude whether a message you received originates from who you think it came from at all, or whether someone replaced part of it with something different.
PGP addresses all of this in theory by offering both end-to-end encryption and a means of signing messages. That means you know for sure that the message you received cannot be read by anyone intercepting the message, and the message really originates from who you think it came from and wasn't changed.
The problem is that for this to work, two prerequisites must be met:
- The other person must use PGP.
- You must have the other person's public key and you must be 100% certain that this is the genuine key.
The first point already pretty much settles PGP's benefits for the "real world". Hardly anyone uses PGP. Your aunt Sally doesn't, your bank doesn't, your electric supplier doesn't, and XYZ doesn't either. Which means you just aren't getting to use PGP, except with a few geeks.
The second point bears the whole lot of problems that SSL/TLS has, too (as explained e.g. in that Defcon Youtube video in cremefraiche's answer), except the chain of trust in PGP is more of a "hobbyist" thing, if I'm allowed to call it that. This may actually be a good thing, but it may as well be a bad thing. Instead of trusting a company that sells certificates for profit, you let your keys sign by a number of... well... people. People you know well, or maybe don't know too well. Depending on who signed their keys, you trust them a little bit more or less.
Unless you meet the recipient at least once in person to exchange keys, you never have a guarantee that you own the correct key (either way).
PGP will hide what you are telling someone, but it will not hide who you mailed, or that you sent a mail at all (well, it can hardly do that, can it). The mere fact that you communicate with people may however already be important (even more so if you communicate using encryption).
An important consideration is that since the vast majority of people doesn't use end-to-end encryption, you are automatically on the bad guys' (bad guys = government agencies) suspect list if you do. After all, if you use encryption, you have something to hide, so you are most probably a crimial, or worse. No such thing as a presumption of innocence exists, outside fairy tale books (even if your constitution says something different).
So, when you plan your next bomb strike, it is probably a good idea not to coordinate your terror cell's weekly meetings via email and use PGP because the NSA will make you a priority target. That doesn't automatically mean you will get waterboarded, but it means that you will be subject to much more detailled profiling and a much more thorough individual analysis.
Depending on what their profiling shows (depending on where you live, who you talk to, what happens on your bank account, where you travel to, what communication pattern you have, etc.), this may result in anything from "nothing happens" to "guys with masks beat the crap out of you so you reveal your passwords" or "wake up in a black camp".
Luckily, for most people, it's the "nothing happens" flavor, but you never know.