There have been some truly impressive writeups on these works (the book and the film). /me bows to
DejaMorgana,
graymocker and
Jackson Mayhem. I just wanted to inject a few tidbits that rolled to the edge of the table in the critical feast above.
First, I'd like to address the point that Verhoeven's version lacks one of the central pieces of the book - namely, powered armor. DejaMorgana's well-done dissection of the military laughability of the movie serves to support the notion that this storyline in some manner rests upon the powered armor. I'd like to expand on this and tie it into the sociopolitical commentary angle.
Starship Troopers is, in many senses, about a war that never happened. It's about a war between the 1950s Heinlein-idealized New Democratic Man and the Godless Communists, but not in the form of the Soviets - rather, in the form of the Chinese Communists, a more monolithic and 'faceless' threat than the USSR ever was. Moreover, the one resource that the PRC seemed to have in infinite numbers, the thing that gave them an 'edge' in a territorial war with the West, was population. They simply had enormous numbers of soldiers. The soldiers were poorly equipped, and not as able as their Western counterparts to wield firepower due to this. Furthermore, in the 1950s American view of communist indoctrination, blind obedience to orders was believed to be a large component of their society. This was seen as an advantage in a military environment.
A large portion of the book is concerned with the training and indoctrination of the cap trooper - in this case, Juan Rico and colleagues. Heinlein's central theme can be seen in the following quote, badly paraphrased from memory:
"It takes a minimum of eighteen months to train a human to fight as an integrated member of a team. Bug warriors are hatched able to do this. If a thousand Bugs die for every MI who falls, it's a net victory for the Bugs."
In other words, the very qualities that make the New Democratic Man so powerful in civil society - independent thought, questioning of authority (note: this is not the same as distrust of authority), and individual strength of will and mind - are all counterproductive to his acting as a member of a unit.
On top of that, it has taken eighteen years (minimum) to train said NewDem to be this Renaissance Man, capable of participating in the government and industry of his society. In other words, this individual is valuable. He or she is impossible to recreate, and difficult to replace. To protect this valuable person, and to allow them to fully exercise the advantage of their technology-rich and resource-wealthy society and industrial complex, Heinlein not only made them fight as individuals-in-a-team but gave them the powered armor. This armor is the final piece of the 'individuals are valuable' equation. Every description of the stuff harps on how it makes one person (that is, one person who is capable of using it and acting as a team member) the equivalent of dozens or hundreds of not only individual soldiers not so equipped, but even today's war machines - "It's not a tank, but a single trooper could have singlehandedly taken on and disposed of a regiment of those silly things."
So, to recap - on one side of this titanic struggle, we have the humans. They field smart, trained, strong-willed and capable warriors, seasoned with eighteen years of training in everything from how to move their limbs to History and Moral Philosophy. Their warriors carry on their backs the sum total of the technology of destruction - able to carry out immense physical feats of war. They are able to smite as Gods, and trained to decide as Gods (at least, the officers are) on the battlefield.
Against them, the Arachnids field a force of infinitely-replaceable moving parts - the Bug warriors and workers. Created 'on demand', the Bug is not so much a warrior as it is ammunition. The struggle is designed to demonstrate that the New Democratic Individualist, armed with the riches of technology, is able to defeat the Communist leader, armed with the lives of his subordinates above all else. That is, it's futile to try to send dominated slaves against the American! While you can pile up enough bodies to take down the New Dem soldier, you can't pile up enough bodies to take down their system - and their system is composed of the ideas and actions of the individuals.
This is why (in my opinion) so many feel that the powered armor is so crucial to the proper telling of the tale. It allows for a single, critical storytelling trick to take place. In almost every confrontation in the book, Mobile Infantry engage vast hordes of the enemy alone. They are working as a team, with others in their unit invisible over the horizon, or hidden behind buildings, or what-have-you, yes; however, they fight alone. They have to; in one briefing, Rico notes that his weapons choices in anything other than a carefully planned, mobile raid are severely limited, because their power means that firing at anything not close and grounded endangers cap troopers over the horizon. This reinforces the entire metaphor alone. In the opening sequence of the book, Juan Rico proves that he, alone, is equivalent to the nations of the 1950s by not only laying waste to large portions of a city using his suit's built-in weapons, but by choosing to carry out, and implementing, a nuclear strike.
Here is where Verhoeven's version departs so radically. The problem with this model, for film, is that it is boring. If most of the action involves single powered armor suited MI taking on thousands of Bugs, the simple mechanical action of killing Bugs will get boring, very quickly. Rico even tells us that it gets boring for him; he starts inventing ways to do it without wasting ammo or jet fuel, using just his hands when possible. I'm not defending Verhoeven's choices, but I can understand some of them; he's making a movie. Not just a movie, but (in his mind, at least) a satire that rests on its ability to suck its audience into an entertaining sequence of events to the point where they 'miss' the thrust of the script initially. Given this, you simply can't have powered armor; it'll ruin the film entirely no matter what you do.
On another note, one problem with filming powered armor suits is that there is no way in hell you could have a suit that could believably do what those suits can - and still have the viewer be able to see the wearer's face. You can't in the book. While there are technological fixes for this for some forms of environmental encumbrance (see The Abyss for example) there's simply no way to do it here.
Finally, there's the simple question of budget. Each CGI powered armor suit would likely involve a budget similar to that spent on the hordes of soon-to-splat extras that swarmed across the scenes of the movie.
Moving on, I will say (with deference to DejaMorgana) that there is no excuse for the complete and utter ludicrousness of the Federation 'military' in Verhoeven's version. Once the powered armor was removed, there was no need to make the whole crew into the Keystone Kops of War in order to make their situation dire and tense! Basic training looked like a set for a Fox Reality Show: EIGHTIES SCIFI PAINTBALL SURVIVOR COMBAT! Tactics were nonexistent, decisionmaking was stupid, and even the weapons were employed poorly. We're not even going to go into the whole 'massive formations of vulnerable slowly-moving starships' routine.
So, to sum up an excessively long-winded writeup, there are reasons why Heinlein needed powered armor, and reasons why Verhoeven couldn't show it. This doesn't make the movie excusable, as I've noted; it merely illuminates the problem. Personally, I feel that if a sociopolitical satire were what Verhoeven was aiming for, then the combat scenes were almost entirely unnecessary, especially in that form - more suggestive, chaotic, personal experiences of violent dystropy serving to break up more contemplative and explicative sequences would have worked. It worked for Heinlein, after all. There isn't that much combat in Starship Troopers (the novel) - and what there is isn't described in great detail (other than the introductory 'teaser'). Sure, the methods and means are - but not the brouhaha itself.