One word can sum it up: debt.
The US economy was destroyed by US household debt. People owed way more than they could afford on cars, education, credit cards, and especially mortgages.
http://blogs.reuters.com/rolfe-winkler/2009/12/10/households-cut-debt-have-long-way-to-go/ This means people had to spend less to make up for it. Spending less means lower business sales, which means fewer jobs (and lower taxes), and which means consumers have to cut back further.
Politicians of course, are playing the US problem as a government debt problem. Government debt here is high, but not dramatically high (US goverment debt/GDP has been higher in the past without problem for example). So when politicians are attacking the wrong problem, the recovery is going to be slow (not that debt problems are ever fast to recover from though).
In Greece the problem is government debt. They just owe far more than they could ever pay back. Cutting back doesn't solve the problem when the majority of all Greeks are government workers. Cutting back for them to reduce debt means that they fire workers, which leads to a bad economy, lower tax revenues, and MORE government debt.
In Spain the problem is banking debt. Spain's government doesn't owe much, Spain's people don't owe much. But Spain's banks owe far more than they can afford. That means that there is no more lending, no more businesses expanding with loans, no more customers spending with help from loans. The economy crashes. Unless of course the bank debt is bailed out, by Spain, which then makes Spain's government too far into debt to survive.
Other countries are mixes in between the three.
Debt problems can only really be solved with time. Time and pain. Debt gets slowly paid down. You probably can't pay off your education / mortage loans in a year or two. Neither can other consumers, governments, or banks. Most of the attempts to pay it off sooner are either drastic (causing bigger problems elsewhere) or futile (borrowing from your left pocket to pay your right pocket). Time allows debt to be paid off bit by bit.
Of course, spending less and bringing in more revenue helps. But that often means prolonging the economic woes. If consumers spend less, the economy slows making it near impossible for them to raise their revenue (income). If goverments spend less or raise revenue by raising taxes, the economy suffers similarly. If banks loan less or raise fees, fewer people/companies borrow which hurts the economy.