For one thing, I've wondered how long this phrase has been around. It seems highly possible (and even likely) that ทรงพระเจริญ is an example of ศัพท์บัญญัติ, or, words or phrases coined as Thai equivalents to foreign words or phrases. But it's also possible that the Thais were using this phrase before extensive contact with the West began. To date, I haven't found evidence one way or the other.
I also used to wonder about the underlying syntax of the phrase, and whether I was interpreting that syntax correctly. ทรงพระเจริญ is an example of ราชาศัพท์ [รา-ชา-สับ], or royal language--the vocabulary used when speaking or referring to royalty (or deity--the two concepts are closely intertwined in Thai thought). Typically, in using royal language, ทรง [ซง] is placed before common verbs to make them royal. Many verbs have specialized royal equivalents, though, in which case ทรง is usually unnecessary.
For example, when your average Joe is hungry, he will typically กิน ทาน or รับประทาน; a monk will ฉัน; but royalty will เสวย. Because there's a special word for it, ทรง isn't strictly necessary (but you'll still sometimes see ทรง used with royal verbs anyway). There are thousands and thousands of verbs, however, and using specialized alternatives for every one is difficult. That's where ทรง comes in handy. It still sets the agent of the verb apart as royal, but easily allows for an unlimited number of actions, such as ทรงเป็น ทรงทราบ ทรงเปิดเผย, etc. In this case, เจริญ means to grow or age. We see it in common language in the elaborate phrase เจริญเติบโต.
The part of ทรงพระเจริญ that I wondered about more, though, was the combination of both ทรง and พระ before a verb. I didn't recall seeing this kind of construction very frequently. As it turns out, it's not entirely uncommon, but it seems to appear as ทรงพระราช- [ซง-พระ-ราด-ชะ] more often. Other examples include:
ทรงพระราชทาน = to give/bestow
ทรงพระราชนิพนธ์ = to write/compose
ทรงพระราชสมภพ = to be born
Any of these can be used without ทรง, though, and in fact, apart from ทรงพระเจริญ, I haven't found any other ราชาศัพท์ phrase that uses ทรงพระ without ราช attached. I'm all ears (eyes?) for suggestions.
Now a bit more about the syntax. If this phrase is like its English counterpart, then its an imperative phrase, or, in other words, a command. That isn't to say it's rude or forceful, simply that when we say "Long Live the King," the grammar of the phrase is commanding him to live long. In Thai, commands can either be marked or unmarked, which result in varying levels of forcefulness. Your basic (non-forceful) command is usually grammatically unmarked. For example, if I want to tell you "come here," I can just say มานี่. This is the form that ทรงพระเจริญ takes. A basic unmarked imperative.
A more forceful command uses the auxiliary จง, although this isn't used much in colloquial speech. Therefore we also see จงทรงพระเจริญ, which in this sense is kind of like the exclamation point on the phrase, if you will.
It's also very common, though, to see ขอ or ขอให้ at the beginning of the phrase, too, both as ขอ(ให้)ทรงพระเจริญ and ขอ(ให้)จงทรงพระเจริญ. When it's left off, it's still understood as if it were there, as opposed a literal command. In a segment of her TV program ภาษาไทยวันละคำ*, Dr. Karnchana Nacaskul had this to say about ทรงพระเจริญ:
"อาจใช้เป็นคำถวายชัยมงคลแด่พระบาทสมเด็จพระเจ้าอยู่หัวและสมเด็จพระบรมราชินานาถ มีความหมายไปในเชิงว่า ขอให้มีสุขภาพดี ร่างกายแข็งแรง และมีอายุยืนยาว"Here Dr. Karnchana limits the phrase to the king and queen, but I've seen it used with, for instance, the prince and Princess Sirindhorn, especially near their birthdays. I also found instances on the web using the phrase with the future heir, the prince's youngest son, who is now just over 2 years old.
"It may be used as an expression of blessing for His Majesty the King and Her Majesty the Queen, having the meaning along the lines of, 'May you have good health, a strong body, and a long life.'"** [My translation.]
Here's a breakdown of Google hits for different versions of the phrase:
ทรงพระเจริญ = 746,000
จงทรงพระเจริญ = 399,000
ขอทรงพระเจริญ = 62,900
ขอจงทรงพระเจริญ = 333,000
ขอพระองค์ทรงพระเจริญ = 276,000
ขอพระองค์จงทรงพระเจริญ = 76,400
ขอให้พระองค์ทรงพระเจริญ = 162,000
ขอให้พระองค์จงทรงพระเจริญ = 23,700
Most of these results are overlapping, since every one of them contains the smaller phrase ทรงพระเจริญ. But it shows us which phrases (in the world of the web) are more or less commonly used.
There are also several variations for what comes after ทรงพระเจริญ (if anything), but ยิ่งยืนนาน is perhaps the most common (ทรงพระเจริญยิ่งยืนนาน turns up 272,000 Google hits).
*This program was a 1-2 minute segment that ran after the news on Thailand's Channel 3 from 1984 to 1994. The entirety of the program was compiled into one volume and published by Chula U Press in 2005.
** ภาษาไทยวันละคำ ฉบับรวมเล่ม, p. 285.
[Hat tip to David for the post suggestion]