Special unit insignia in every army are revered by the men within that unit, for starters. Every armed force has some insignia that distinguishes them from all the others, and that they use to identify themselves as the elite (since every outfit in the history of ever considers themselves the elite).

However, it's certainly true that the Romans placed a great deal more importance on their standards than we would today. Or did they? In Napoleonic armies the loss of the colors was a total disgrace, one that a regiment would never wipe from its history, even if they managed to recapture their colors, unless they captured the colors of an enemy regiment. The loss of the colors was so important that countries would be willing to buy them back from each other at absurdly high prices, or trade them for prisoners and so forth. It's a similar situation as with Rome, in that the colors symbolized the country that the armed forces were attempting to defend and protect itself.

But with Rome it's even more. The first state to our knowledge that employed standardized battle standards (say that five times fast) was the Macedonian state under Philip, in which each battalion of the Phalanx was given a standard, although we have no idea what these might have looked like. It's almost certain, however, that the Theban army under Epaminondas also employed standards, and it's possible that they were already in widespread use since at least the end of the Peloponnesian War. The Romans were using them from an early date, although we don't know what the standard of each maniple during, say, the Punic Wars might have looked like. The Roman standards as we know them were introduced by Gaius Marius, who personally gave to each of the legions under his command and that he raised a silver (later gold) eagle and some other standards (the eagle was the important one, though).

So why did Roman armies have even more reverence for their standards than the armies of Napoleon or other similar ones? There are a lot of reasons, actually. Most obviously, the standards symbolized not only Rome but her very traditions and essence, in a way that the King's Colors never did. The eagle and the various other insignia represented in particular various ritual aspects of the Roman state and people. For example, the eagle is the symbol of Jupiter, and by carrying around an eagle to watch you, Jupiter quite literally is there watching over the legion, rather like the way that various gods fight beside the champions in Homer. And that ritual aspect is another important reason, probably more important in the minds of your average soldier. Understand that in the ancient world religious and secular life are not separated the way they are today. They are one and the same, since the activities of every day are surrounded by a series of rituals that you naturally undergo. We still go through most of these rituals, even though we don't realize it. In the ancient world they were consciously recognized as rituals and interconnected with religious worship. The Roman standards are very obviously sacred implements, and are often addressed using language that would be appropriate for sacra, even if they are not generally called by that term. This was very consciously recognized in Roman society, as evidenced by the fact that after the organization of the imperial cult the image of the emperor was added to the signa, as a sacred icon in the same way that the eagle was (also, the signa are quite frequently called sacred, even if they are not the sacra overtly, the sacred implements used in the worship of a god in any particular cult, that are unique to that cult). Later, under the Principate, the standards came to symbolize Roman civilization as opposed to the frontier, and their loss was obviously a serious hit to a legion.

Now as for the lengths that Romans would go to recover eagles and so forth, that's greatly exaggerated. I have something of a hunch that you're referring to the story about the Ninth Legion's eagle, and the story that they all just up and decided to go north into Pict-country to recover their eagle and were destroyed along the way. That's an absurd story. There's absolutely not one shred of evidence to suggest that such a thing occurred, and the story is the result of the fancy of Rosemary Sutcliff in her work of fiction, The Eagle of the Ninth. What really happened to the Ninth Legion is unknown, they just disappear from the roll of legions. Which isn't surprising, since the roll never tells us what happens to a legion, it just says that that legion is no longer on the roll. Roman legions didn't just up and decide to march into hostile territory to recover an eagle and not for any particular strategic importance, and if anyone could plausibly explain to me how on earth an eagle captured by Boudicca a hundred years earlier could have ended up in Pict-country when the Iceni and their allies were hostile to the Picts and were quite isolated from them that would be nice. The Romans would go on expeditions to recover eagles, but not without another purpose. For example, during Germanicus' campaigns in Germania, his troops would defeat enemy forces and plunder their sanctuaries, in which there would often be some captured spoil dedicated to the god--often a standard (again with the ritual aspect of those things). In particular, Germanicus recovered two of the three eagles lost at the Teutoburg Forest, although these victories were pretty minor compared to his crushing defeat of Arminius and the capture of Arminius' wife.

It's important to note that the importance of the standards to an individual legion was not very great until the Principate, when the number of legions was standardized and they became permanent. We don't really find Caesar's legions or the troops fighting during the Punic Wars freaking out in quite the same way. They're upset, sure, but not because they've somehow been disgraced, at least not as much as later legions. The importance of the standards until the Principate rests primarily in their ritual importance and their symbolism of the Roman state and her gods. Loss of the standards means that they are cut off from the Roman gods and cannot be properly worshiped. It's not until much later that it's the supreme disgrace of a legion and considered even close to treason.