Chief Justice Roberts wrote the opinion. Upholds Individual Mandate as a tax under Congress’ taxing powers. Apparently a complicated opinion. Others are more equipped (and have the time) to analyze, but feel free to comment!
ADDENDUM (snarky version): Roberts joined with the courts liberals, so it was 5-4. Not quite the 5-4 decision anyone anticipated, to be sure. What are liberal supporters of the Health Care act going to say about Roberts now? Does this mean the Supreme Court is all-of-a-sudden legit again?
ADDENDUM (serious version): Some are arguing that by upholding the mandate by calling it a tax while expressly ruling that it’s NOT legit under the Commerce Clause, CJ Roberts has managed to give liberals a political win while also pushing back against big government overreach, which is something conservatives like. Jay Cost:

First, the Roberts Court put real limits on what the government can and cannot do. For starters, it restricted the limits of the Commerce Clause, which does not give the government the power to create activity for the purpose of regulating it. This is a huge victory for those of us who believe that the Constitution is a document which offers a limited grant of power.
Second, the Roberts Court also threw out a portion of the Medicaid expansion. States have the option of withdrawing from the program without risk of losing their funds. This is another major victory for conservatives who cherish our system of dual sovereignty. This was also a big policy win for conservatives; the Medicaid expansion was a major way the Democrats hid the true cost of the bill, by shifting costs to the states, but they no longer can do this.
Politically, Obama will probably get a short-term boost from this, as the media will not be able to read between the lines and will declare him the winner. But the victory will be short-lived. The Democrats were at pains not to call this a tax because it is inherently regressive: the wealthy overwhelmingly have health insurance so have no fear of the mandate. But now that it is legally a tax, Republicans can and will declare that Obama has slapped the single biggest tax on the middle class in history, after promising not to do that.

UPDATE: Key components of Roberts writing on the SCOTUS ruling (PDF) upholding individual mandate (after the jump):

Why mandate is NOT legitimate under the Commerce Clause:

CHIEF JUSTICE ROBERTS concluded in Part III–A that the individual mandate is not a valid exercise of Congress’s power under the Commerce Clause and the Necessary and Proper Clause. Pp. 16–30. (a) The Constitution grants Congress the power to “regulate Commerce.” Art. I, §8, cl. 3 (emphasis added). The power to regulate commerce presupposes the existence of commercial activity to be regulated. This Court’s precedent reflects this understanding: As expansive as this Court’s cases construing the scope of the commerce power have been, they uniformly describe the power as reaching “activity.” E.g., United States v. Lopez, 514 U. S. 549, 560. The individual mandate, however, does not regulate existing commercial activity. It instead compels individuals to become active in commerce by purchasing a product, on the ground that their failure to do so affects interstate commerce. Construing the Commerce Clause to permit Congress to regulate individuals precisely because they are doing nothing would open a new and potentially vast domain to congressional authority. Congress already possesses expansive power to regulate what people do. Upholding the Affordable Care Act under the Commerce Clause would give Congress the same license to regulate what people do not do.

Not legal under “Necessary and Proper Clause”:

Nor can the individual mandate be sustained under the Necessary and Proper Clause as an integral part of the Affordable Care Act’s other reforms. Each of this Court’s prior cases upholding laws under that Clause involved exercises of authority derivative of, and in service to, a granted power. E.g., United States v. Comstock, 560 U.S. ___. The individual mandate, by contrast, vests Congress with the extraordinary ability to create the necessary predicate to the exercise of an enumerated power and draw within its regulatory scope those who would otherwise be outside of it. Even if the individual mandate is “necessary” to the Affordable Care Act’s other reforms, such an expansion of federal power is not a “proper” means for making those reforms effective. Pp. 27–30.

It’s a tax:

…the individual mandate must be construed as imposing a tax on those who do not have health insurance, if such a construction is reasonable. The most straightforward reading of the individual mandate is that it commands individuals to purchase insurance. But, for the reasons explained, the Commerce Clause does not give Congress that power.It is therefore necessary to turn to the Government’s alternative argument: that the mandate may be upheld as within Congress’s power to “lay and collect Taxes.” Art. I, §8, cl. 1. In pressing its taxing power argument, the Government asks the Court to view the mandate
as imposing a tax on those who do not buy that product. Because “every reasonable construction must be resorted to, in order to save a statute from unconstitutionality,” Hooper v. California, 155 U. S. 648, 657, the question is whether it is “fairly possible” to interpret the mandate as imposing such a tax, Crowell v. Benson, 285 U. S. 22, 62. Pp. 31–32.
4. CHIEF JUSTICE ROBERTS delivered the opinion of the Court with respect to Part III–C, concluding that the individual mandate may be upheld as within Congress’s power under the Taxing Clause. Pp. 33–44.
(a) The Affordable Care Act describes the “[s]hared responsibility payment” as a “penalty,” not a “tax.” That label is fatal to the application of the Anti-Injunction Act. It does not, however, control whether an exaction is within Congress’s power to tax. In answering that constitutional question, this Court follows a functional approach,“[d]isregarding the designation of the exaction, and viewing its substance and application.” United States v. Constantine, 296 U. S. 287, 294. Pp. 33–35.
(b) Such an analysis suggests that the shared responsibility payment may for constitutional purposes be considered a tax. The payment is not so high that there is really no choice but to buy health insurance; the payment is not limited to willful violations, as penalties
for unlawful acts often are; and the payment is collected solely by the IRS through the normal means of taxation. Cf. Bailey v. Drexel Furniture Co., 259 U. S. 20, 36–37. None of this is to say that payment is not intended to induce the purchase of health insurance. But the mandate need not be read to declare that failing to do so is unlawful. Neither the Affordable Care Act nor any other law attaches negative legal consequences to not buying health insurance, beyond requiring a payment to the IRS. And Congress’s choice of language—stating that individuals “shall” obtain insurance or pay a “penalty”—does not require reading §5000A as punishing unlawful conduct. It may also be read as imposing a tax on those who go without insurance. See New York v. United States, 505 U. S. 144, 169–174. Pp. 35–40.
(c) Even if the mandate may reasonably be characterized as a tax, it must still comply with the Direct Tax Clause, which provides:“No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or Enumeration herein before directed to be taken.” Art. I, §9, cl. 4. A tax on going without health insurance is not like a capitation or other direct tax under this Court’s precedents. It therefore need not be apportioned so that each State pays in proportion to its population. Pp. 40–41.