The first thing that must be done (lest it be thought that I have a secret agenda) in this article is to define some notation. Throughout this article, Latin words will be placed in italics. Since I am restricted to 7-bit ascii, this will be indicated by enclosing italicized words in underscores. For example, exempli gratia is in italics. This formalism is necessary to prevent Latin from sneaking into the article incognito. [Of course, HTML provides italics so I put them back in - Sz.S.]
Let me stress that I have nothing against Latin qua Latin. It is a noble language, and indeed it is the root of approximately three-quarters of the English lexicon. In fact, there are quite a few words that are now considered to be English that have come straight from the Latin. An example is exit. In theatre scripts, one often sees the variant exeunt omnes, but then theatre people have always been noted for carrying on like all get out. Show me a playwright and I will show you an ego.
I have no problem with the use of Latin per se. For example, how many people realize that by naming their dogs Rex or Fido, they have ipso facto unwittingly named them in Latin? 
There is a disturbing trend, however, for Latin to find its way into English sentences where there is no bona fide justification for it. Often a speaker (or an author) will use a Latin phrase in an attempt to flaunt their education. Dropping Latin phrases into one's sentences (quid pro quo, deus ex machina, et cetera) is in many ways a de facto equivalent in academic circles of the name-dropping practiced by celebrities and their hangers-on. Rather than trying to suggest that they were almost caught in flagrante delicto with Claudia Schiffer, the academic will drop the occasional Latin phrase in the hope that his listeners will think that he is an emeritus professor who graduated summa cum laude from literae humaniores at his Alma Mater, Oxford.
Of course, attempting to ad lib. with Latin phrases in English is not without risk. The onus is on the speaker to avoid errors. Imagine the derision to which an airline official would be subjected if he claimed that a bomb had been allowed onto a plane (in the luggage of a person who did not board the flight) due to a manifest non sequitur.
One must also be very careful about spelling. I have seen people write things like add nauseum [sick], which looks like an instruction from a recipe incorporating Vikings. Errors such as this will very quickly result in one becoming persona non grata with the very people one was setting out to impress.
There is a more subtle trap for the unwary Latin user. Occasionally an innocent Latin phrase can sound quite rude when heard by native English speakers. I am sure that Queen Elizabeth II would never have used the expression annus horribilis if she had considered the sort of puns that the tabloid press were likely to come up with a posteriori.
Do not be totally discouraged. I do think there is a place for the occasional bit of Latin-dropping. Any attempt to eliminate Latin from English usage would quickly result in a reductio ad absurdem. My advice is simply this: Be careful. Be sure of your facts before you seize the day and use carpe diem in a sentence.
--- FINIS ---
Postscriptum: The number of Latin words that are used in this way is very large. I could continue producing examples (for instance, ad infinitem) forever. I think, however, that I have proved that which had to be proved. Ergo, I see no need to discuss phrases such as quod erat demonstrandem.
 The translations being "King" and "I am faithful", retrospectively.