The greatest beneficiary of America's war against Iraq has been Iran. We made a mistake attacking Iraq after 9/11, and in doing so, we did Iran a favor by removing Saddam Hussein. Sadly, the invasion did nothing to increase our own safety, because there has never been a substantial connection between 9/11 and Iraq.
Thus, the short-term results of Bush II's Iraq war are that thousands of American soldiers have died while Iran's influence has increased; and we have spent trillions of dollars invading a country that did nothing against us. However, we can never admit such profound folly, so the U.S. is determined to ensure that our initial mistake--invading and occupying Iraq--does not compound itself. Allowing Iran to install its own power base in Iraq (or Afghanistan) would compound our initial mistake, and the U.S. is doing whatever it can to stunt Iran's influence.
Why would Iran care about Iraq, and why would Iraqis care about Iran? Muslims are typically either Sunni or Shiite/Shia. Within Iran, almost all Muslims are Shiite--just like the majority of Iraq's Muslims. Outside of Iran, however, almost all Muslims are Sunni. In fact, Iran is surrounded by Sunni Muslim countries like Saudi Arabia, Pakistan, etc. If Iran is able to extend its influence into Iraq and make Iraq an ally, it would finally have a Shiite neighbor. From an American perspective, the more Iran's neighbors are friendly with Iran, the more difficult it will be to stunt Iran's influence. Now might be a good time to remind everyone that Iran contains the world's second largest natural gas reserves and third largest petroleum reserves.
To minimize Iran's influence, the United States has been helping paint Iran as a rogue nation. Basically, the United States government has been releasing information to create support for an attack against Iran if Iran continues to extend its influence over Iraq. For example, at one point, Yahoo's homepage showed a picture of a new Iranian bomber drone almost the entire weekend. Despite the fact that Iranians are model citizens in the United States (look up who founded eBay), you will almost never see the word "Iranian" in a story without some negative connotation. The media's quest to dehumanize Iranians is in full effect. After all, one can't have a war without first making the enemy into "the Other."
The real issue is the extent to which Iran has the capacity or willingness to attack American soldiers or Americans. A country that has been around for 3000+ years probably doesn't have a death wish. Even if it did, and even if Iran managed to get nuclear weapons, it still needs to transport them effectively. As North Korea's failed missile tests demonstrate, it is much easier to make a weapon than it is to deliver it accurately.
Overall, it is hard to believe that the Iranian government would be capable or stupid enough to directly attack any American soldier or civilian. Even when the Iranian government has captured American civilians or possible CIA assets, it tends to return them unharmed. (This pattern holds true in the capture of the American embassy in 1979 as well as the more recent American hikers, who were arrested when they entered Iran without proper authorization.) However, if the current Iranian government extends its influence over Iraq and Afghanistan, it may use sections of these countries as proxies or buffer zones. In other words, doing nothing would allow an extension of a government hostile to American interests. And therein lies the problem.
Ironically, without Saddam Hussein to keep the Iranian government in check, the Middle East has managed to become more complicated. Under Saddam Hussein's Iraq, the Ba'ath Party dominated politics. The Ba'ath Party was secular, not Muslim. By killing a secular leader, we allowed more religiously-committed factions to spread their influence over Iraq. Any American who thought invading Iraq and toppling Saddam would show "those Muslim terrorists" is misguided. Maybe next time, we'll do more research and question our government when it tells us war is good.
Also, most Americans don't remember the Iran-Iraq War, but back in the 1980's, Saddam Hussein waged a bloody war against Iran and used chemical weapons against Iranians. I bring this up to remind Americans that Saddam Hussein was once our friend--and Iran's worst enemy. By removing Saddam Hussein and not achieving broad consensus on a rebuilding plan (such as the Marshall Plan), we've managed to create more problems. And this time, war won't be quite as simple. Unlike Iran, Iraq was never a tightly-knit, sovereign state. In fact, modern-day Iraq is basically a post-WWI British creation. In contrast, Iran has been together for 3,000 years and has never been occupied by a foreign power. I doubt Bush II's White House properly considered the downsides of invading Iraq. The American people were stunned by 9/11 and needed a show of force. It got one. And we're still dealing with the consequences years later.
Conclusion: the only way America can claim a victory against terrorists is if it eradicates the Taliban and al-Qaeda. The Taliban and al-Qaeda are in Pakistan, Yemen, Somalia, and parts of Afghanistan. The Iranian spectacle is just a side-show of our own making.