U.S. Government DID save American International Group (AIG) from bankruptcy, since it was considered too big to fail, actually: a lot of financial institutions were insured by AIG. This Investopedia page is a nice summary on the topic about AIG's bailout. Here (Investopedia again) about Lehman Brothers, that became really too much leveraged and exposed to the subprime business.
Personally, I think that it ALL begun with the deregulation driven by the FED and its chairman Alan Greenspan (Wiki) during the '90s and earlier '00s, who was too much confident about the self-correcting capacity of the markets.
The rating agencies are paid from financial institutions (for example) to give a rating to the firm, the products sold, etc. During the decade before the financial crisis, there were very too much money involved into the business, and it was convenient for everyone to give the highest rating possible also to very bad products, since this led other money in the pockets of financial institutions, without thinking to the consequences. The leaders of that companies are, in any case, safe from the losses: they got millions (even dozens of millions) in "severance pay" after the collapse of the financial markets.
EDIT: Probably, sooner or later, the crisis would have started even with the bailout of Lehman Brothers, since the situation was very unsustainable (not only for the questioned bank): you can read in this NY Times article the proportion of the help that U.S. Government gave to both the biggest banks and minor financial institutions. The literature about the topic is very wide and you can find a lot of data (losses, debts, magnitude of subprime mortgages and related derivatives products that financial institutions all over the world bought) and explanations (conspirancy theories appear very plausible to this situation, such as the one explained by @InnocentR on the comments).