I've always had an interest in "conspiracy theories" and have done my fair share of research on this one. Jordan Maxwell, cited above, is generally a decent source. The man has done countless hours of research on symbols and their meanings and the field is better off thanks to it. He does, in my opinion, sometimes "go to far" and looks a little to deeply into this things. This is one of them.
I haven't studied the Dollar Bill Theories as extensively as I have other theories (JFK, Pearl Harbor, Iraq, WWI etc) so some of what I type below may not be complete. If I'm missing something it is due to ignorance, not intention...
First I will tackle the Star of David. Like Biokemist pointed out, this star has been used on a lot of American coinage, and I'm willing to bet on a lot of other country's coins too. It is simply a nice looking star, simple and elegant at once. There is no way this has any relation to the contemporary Zionist State centering around Jerusalem. For one, the modern Zionist movement was simply not around during the times many of these coins were designed. Second, the movement by the 1930s (the time of the design of the dollar bill) was no where near as influential as it is today and would not have been capable of planting its symbol on the currency of the US. Third, FDR is a known anti-Semite (as were many of his contemporaries) who would never even dream of such "Jewishness" on the dollar bill. A Zionist connection seems pretty far fetched.
The incomplete pyramid is a brilliant symbol. Yes, the pyramids of Giza have often been used as Masonic symbols. Think of it for a second - what is the greatest stone masonry work ever accomplished? Why the pyramids of course! Though they have never claimed the work as one of their own, the symbol of the pyramids has become theirs. However, one need not look that far into it. The Great Seal (to which the pyramid image is on the reverse) was designed long before FDR by a man named William Barton in the 1780's. Barton has never been claimed by the Masons nor has he been credibly accused by non-Masons. If the pyramid is not Masonic, then what does it mean? It is still rather strange to see a pyramid on the very symbol of the U.S.
The pyramid is most likely symbolic of the "greatness" of America or, considering it is an incomplete pyramid, the potential greatness. A great monument of Man's past used to symbolize the hope and enthusiasm of Man's future...a most poetic vision if I've ever seen one!
The Eye in the keystone of the pyramid has a long history in the world of symbolism. The eastern Mediterranean world (think Greece, Turkey, etc) used this Eye as a way to ward of evil. I'm a little lacking in my information regarding the practice, but the eye represented the very concept of evil, hence "the evil eye". If one would wear the Eye as a piece of jewelry or on your clothing or paint it across the front door, evil would be chased away from you and yours. The practice is still used today - I have a glass bead painted with the Eye a friend of mine brought to me from a recent trip to Greece.
That said, in the times of the Renaissance and the Enlightenment of Western Europe, the Eye came to be used as a symbol for the Divine. A "he sees you when your sleeping, knows when your awake" sorta thing, as well as a dodge of the very practical question "what does God look like?" Masons were quick to adapt this meaning as it is a key believe in their system to recognize the existence of a higher power but not to pass judgment upon others' beliefs. By using a symbol like the Eye, there was no need to exclude any of the members who may have believed in the Christ, Allah, Yahweh, any of the Pagan gods, or the great Spaghetti Monster Himself.
The Eye ties in wonderfully with my incomplete pyramid theory. The foundation for greatness has been laid by Man (base of pyramid) but only with the help of God can our full potential be reached (the keystone). I'm not a religious man myself (far from it) but this image is simply beautiful and very powerful.
The Owl is my next tackle. I will say right from the start that I truly hate the owl. It creeps me out. The Owl's main purpose is for counter-counterfeiting purposes. It is very small, incredibly detailed, and hard to reproduce successfully. But why an Owl? Why not an eagle? Or a bear? Or a little picture of Josh Tatum?
Theories abound on this with one of the major ones being a reference to the Bohemian Grove cult, a group which worships a giant Owl and who's membership includes many politicians and powerful men. Weird (and interesting) as this cult is, FDR was not a member. I am not sure, though, when the Owl was placed on the bill. Does anyone know? Was it an original 1935 piece or added later? It could lend some more credibility to the theory if placed on by a member.
More simply and much more likely, the Owl is symbolic of wisdom.
You also get much talk of the symbolism of the Owl as an Orwellian Big Brother type device. Similar to talks of the All Seeing Eye, the Owl sees all and, being wisest amongst beasts, knows all. Not the intention I don't think, but it does fit nicely with the current state of the union, in my opinion at least.
Now, we come to the three Latin phrases.
"E Pluribus Unum" literally meaning "Out of Many One". Designed in 1776. 13 separate states (many) join together in union (one). Has been attributed to New World Order groups as the concept the same (many countries becomes one country). Point taken.
"Annuit Coeptis" literally meaning "He Approves Our Undertaking". Designed in 1782 ."He" = god and "our undertaking" = the Republic. Quite a common theme for governments to justify themselves through Divine Right, as silly and nonsensical as it may seem.
"Novus Ordo Seclorum" literally meaning "New Order of the Ages". Designed in 1782. The Republic is dreamed to be a new form of government that will sweep the world and change it, entering mankind into a New Order. Often translated as "New World Order" though the Latin word for "World" is "Mundi".
All three phrases have been attributed to the Roman poet, Virgil.
A Masonic design is possible. The Masons trace their origins back to ancient Jerusalem and the construction of the First Temple and often use the Star of David as a tribute to this fact (whether they actually build the Temple is a great debate but of little importance here). The Eye is used by Masons as a symbol for God and the Pyramid is a symbol of the greatness of the stonemasons of the past. The Owl has no connection as far as I can tell. Lastly, we have the number "13" which appears EVERYWHERE on the dollar bill. Traditionally, it is attributed to the 13 original States (not colonies but states; there were many more than 13 colonies despite what you've read in 5th grade history class). 13 steps on the pyramid, 13 letters in "E Pluribus Unum" and "Annuit Coeptis", 13 stars, 13 bars on the shield, 13 leaves, and 13 arrows. Could this all by a tribute to the 13 states? Short answer, YES! Long answer....
13 is an unlucky number in mainstream society. It is also a Masonic number that traces itself back to THE Friday 13th, October 13 1307. That was the day the Templar Knights, long considered the forerunner to the modern Masons, were wiped out by the French King and his allies. This is cited as proof the Masons are behind all this.
The 13 are all there, but a problem is encountered. To go through so much trouble hiding all these 13's why not replace "Novus Ordo Seclorum" with a phrase with 13 letters so to keep the symmetry? Why is it that there are 13 letters in "Annuit Coeptis" only if you separate the "oe" which, in Latin, are connected as one letter? If 13 is part of some mad conspiracy to rule the world, why did the US briefly abandon the 13 stripes in the flag and make the move to 15 when Kentucky and Vermont entered the Union? To many questions for this to have any significance other than the states theory.
Possible, but not as significant as some claim. The Masons are not as organized as many claim and the group has never attempted to seize power here, in France during the Revolution, or in any other time or place. Many of their members are powerful and their influence is far reaching but that does not mean they rule the world, and it certainly does not mean they would reveal themselves on a piece of paper called "a dollar bill".
Other money related conspiracies have been proven true however. The Hunt brothers hoarding of silver, the 1913
Liberty nickels, the establishment of the Federal Reserve (and their current practices depending on your political viewpoints), the very concept of Fascism as defined by Mussolini, and the counterfeiting of 1990 $100 dollar bills can all be labeled conspiracies involving currency. With so many real conspiracies out there, I suggest not looking to deeply into this one.