I also want to add my apologies - I was not sufficiently clear above that I followed the distinction originally made; it was sloppy of me to use "please" in my first post. And just to be clear, I should also point out that I was *not* suggesting that we go around translating "quaesumus" as "please" in the Mass (I am no fan of ICEL).
To follow up on Jeremy Holmes's prior comment, I should point out that "quaeso" and "quaesumus" occupy something of a gray zone between expression of entreaty and particle of entreaty. By about the time of Christ, "quaeso" had ceased to exist as a normally functioning verb in that form. By various sound changes, the verb had changed from "quaeso"/"quaesumus" to "quaero"/"quaerimus" - that is, it became the regular old verb "quaerere" (to seek, ask). The archaic s-forms were from about this point used only in the parenthetical manner, as a sort of semi-particle of entreaty. But I imagine that they were close enough to the newer forms that your reasonably intelligent Roman would still have had a sense of their origin & meaning. This is why I would say that they were in a sort of middle ground, rather than being true particles.
And if we want to translate the absolutely literal sense (rather than the function) of "please" into Latin, it would be "placeat". Admittedly, "placeat" was not used in the same way that we use "please", but they have the same ultimate meaning.

In the blog post, Jimmy said: "Please" is what's known as a particle of entreaty--that is, a short word that never changes its form and that is used to make requests (or commands) sound more polite. If I understand rightly, he means that "please" used to be a proper verb, but by customary usage has lost its verb denotation.
Above, Christopher proposed several possible Latin "pleases", and mentioned: In this category, a couple noteworthy contractions occur in colloquial speech: "sis" (= "si vis", not to be confused with "sis" the subjunctive of "es") and "sodes" (= "si audes"). If I understand Christopher rightly, the reason these contractions are "noteworthy" is that they indicate a change in customary usage similar to what took place in the English "please": that is to say, "sis" probably did not register with a Latin speaker as a verbal phrase, but as a short politeness sound, a short word that never changes its form and that is used to make requests (or commands) sound more polite.
Without a lot more Latin reading than I have done, it would be hard to know whether the same meaning-loss took place with other verbs that were not contracted. For example, did a Latin speaker hear "quaeso" as an actual verb, or did it sound to him like our English "please" (which is identical in spelling to a real verb)? So we cannot discount a proposed Latin "please" word on the grounds that the same form is used elsewhere as a verb.
I've tried to keep Jimmy's distinction carefully in view here; my apologies if I did not succeed!

I'm going to make sure this comes back somehow as a recurring theme in photo caption contests.
By the way, where'd those go?

As noted above, Latin has lots of ways of saying "please".
What did I just say?
In this exchange we are distinguishing between expressions of entreaty and "please." This has been obvious since the original blog posts, in which I acknowledge that Latin has expressions of entreaty and distinguish them from "please." Kindly attend to the distinction.
Please.

As noted above, Latin has lots of ways of saying "please". I could add lots of other ways, but the one not mentioned and very much worth mentioning is to use the subjunctive, which, except in certain cases, English has pretty much discarded.
The problem here is not one of grammar or vocabulary, but of use of the language itself. Simply put, in Latin one says "please" differently than one does in English. Politeness in a language is very much a cultural thing. What may be polite Latin may not be easily recognized as polite English (and vice versa, I might add).
In English we would likely say "Please, Lord..." , but in Latin one would likely use a verb, an adverb, or even a short pharse to render a polite request. Lots of examples come to mind, but two very common forms in the Liturgy and private devotions are: "Quaesumus, Domine" (We beseech Thee, Lord), and "Deprecamur, Domine" (We beg you, Lord).
Now in English these days "begging" is considered a bit low class and I dare say that "beseeching" is right out. So while these phrases may seem a bit odd to many English speakers, they are polite Latin.
Lastly, if you look at the Latin texts in the Liturgy and private devotions, many times they are tripping all over themselves to show humility, even to the point of perhaps getting a bit carried away. (I mean how many "we are not worthy" does one really need in a prayer to get the point across?) As to why this often does not come across well in English is twofold in my opinion. 1) Cultural use of language (as noted here), and 2) ICEL translations often do not reflect the full depth of the Latin.

I appreciate the effort that folks are going to, but some are not quite getting it.
The question is not "Does Latin have ways of expressing entreaty?" it is "Does Latin have an equivalent of please?"
The answer to the first question--as I have already said--is "Yes, every language has ways of expressing entreaty."
What folks have been producing--with things like "Amabo te" and "Quaesumus" and "Si tibi placet" and "Oro" and "Si videtur"--are different methods of expressing entreaty, but none of these are direct equivalents of please. All of them would literally translate into English as something other than "please."
If you want someting that isn't just a method of expressing entreaty but that is a true equivalent of please then you need something that literally translates as "please," and Latin doesn't have anything that does that.
"Please" is a particle (a non-inflecting word) which has lost its denotative meaning so that it operates ONLY as a function word to express entreaty and has NO OTHER MEANING.
If something translates literally as "I ask" or "I beg" or "If you would see" or "I will love you" or "If it pleases you" then it isn't a direct equivalent of "please" because its direct translation is something else. It's only a method of expressing entreaty.
Translating an expression of entreaty as "please" might by okay for the old ICEL which gave us the current liturgical translational monstrosity that we have to deal with, but that isn't what it literally says in the Latin.
The truth is that Latin does not have a literal equivalent for "please," which is why folks cast about for other forms of entreaty looking for "Latin ways of saying 'please.'"

Oh, it wasn't Jimmy at all, but an Anonymous Coward. A thousand pardons.

Also, it might be relevant to point out that English "please" is not really a particle. Or rather, we use it as a particle now, but it is not one originally. It is the imperative/optative of the verb "to please", something which we once expressed simply by using the infinitive form of the verb without the "to".
Perhaps the most familiar example would be "God bless you" (where "bless" is the imperative/optative). In contemporary English, we have lost the sense of verb moods, and so we use auxiliary verbs to reinforce it: so now, we would be more inclined to say (that is, if the expression had not already crystallized) "may God bless you", which means exactly the same thing as "God bless you", but we have added a "may" to set off our "optative/imperative" signals.
Our "please" is truncated from "please you" (the form of the expression which appears, e.g., in Shakespeare). So "please (you)", an imperative/optative form like "bless you", is just an old-fashioned way of saying something which we would now say as "may (it) please (you)". Hence, we can use it both parenthetically: "(may it) please (you), do me a favor"; or with the infinitive: "(may it) please (you) to do me a favor" (although the latter is much less common).
Ultimately, I don't know of any language in the Indo-European family (I don't know anything about Semitic langauges) which actually has a true particle for "please": Romance languages have per favore/por favor (lit. "for a favor"), si vous plais ("if you please"); German "bitte" means "I ask"; Polish "prosze" means "I pray"; modern Greek "parakalo" means "I request" (ancient Greek used expressions like ei dokei, or ei soi philon), and so on. I'd be happy to hear any counter-examples, if anyone has one.
Okay. I'll be quiet now. Hope this was more informative than dull.

Oh, bah. Now I have to go back and find that post, so I can see what Jimmy really said.

Amabo te is not necessarily marked as a feminine as far as I know - Cicero certainly uses it enough in his letters - but it is a rather familiar/colloquial expression; it is found most often in Roman comedy.
Aside from that, there are a couple different ways that Latin has to say "please":
1) parenthetical use of a verb of entreaty, such as "precor" or "oro" (both "I pray" - think of the slightly archaic English phrasing: "What, pray, are you doing here?"), or "quaeso" ("I ask") - so all the "quaeso"s and "quaesumus"es in the prayers of the Mass are roughly a Latin way of saying "please".
2) Expressions meaning approximately "if you will" or "if you please": "si videtur", "si libet", "si vis" and the like. In this categoy, a couple noteworthy contractions occur in colloquial speech: "sis" (= "si vis", not to be confused with "sis" the subjunctive of "es") and "sodes" (= "si audes").

Ed--the Latin used in Church prayers differs from classical Latin, of course, at least in vocabulary. I recently looked up the work purgamentum in a dictionary of classical Latin and found the meaning "dirt, filth"; I looked up the same word in a medieval dictionary and found the meaning, "means of purification"! Not surprising, given that over a thousand years separates the Rome of antiquity from the medieval Church. Languages change.
After poking about, I found that the Vulgate does have an idiom such as Jimmy refers to: "If it please you" (Si tibi placet). See for example Esther 1:19. This translates the Hebrew "If it is good to the king". I'm not a good enough Latinist to know whether this was a proper Latin idiom or something imported from the Bible.

Jimmy--it seems to me that quaeso ("I beseech") or quaesumus ("we beseech") is often thrown into prayers where it doesn't mean anything more than the English "please". Perhaps you or another blog reader who knows more than I do can check me on this.

Latin does not have "please" as we use it. The Romans were not culturally into asking permission for anything. Can you imagine the asking "Please, may we invade your country?" I don't think so.