As far as getting these instruments in too good to be true online scams — with the sour economy — I am seeing more and more people who really want to believe they have come into a financial windfall. When they fall for these scams, one thing is for certain — they are going to be held liable for cashing the items when the scam is discovered. This will certainly include being held financially liable, but can also mean facing criminal charges.
As for counterfeit MoneyGram instruments, although a lot of them seem to be out there, they are not the only items being counterfeited. U.S. Postal Money Orders have been seen frequently in the past, too. Recently, the U.S. Postal Service redesigned their product and has a new page on their site to help consumers verify their product. Counterfeit cashier's checks, money orders, gift and travelers cheques are also known to be frequently counterfeited and used in these types of scams.
If you want to learn more about these scams, I recommend going to fakechecks.org, where you can see some highly visual demonstrations of these schemes. Another good resource on this subject — particularly if you are a victim — is FraudAid. The folks at FraudAid actually provide resources and advocate for people falling for these scams.