Below are four things I used to believe, not that long ago, but have since given up on. I'll follow up -- maybe -- on why I don't believe any of these things any more in subsequent posts. Note that I don't currently believe any of these arguments, though I still agree with several -- perhaps most -- of the premises.
1. Majoritarianism and the Constitution. As a formalist by instinct, I've always been drawn to originalism, at least meant narrowly as a criterion for judges. Laws ought to change their meaning only if the Legislature thinks so, or else we're going to be run by the whims of unelected judges. On the other hand, I've never had much time for the founding fathers or the Constitution per se; on the substance of current issues, whether gay marriage or internet privacy, "what would James Madison do?" is almost never a germane question. (Similarly, one would not expect "What would Barack Obama do?" to be relevant to 22nd cent. debate.) If you put these together, that seems to imply that the constitution should be a lot easier to amend than it is, and that judges should be textualists in their interpretation. At least, this is what one would want in an ideal world: in practice, judges should defer to the executive except in extreme cases.
2. Means-testing. The government wastes rather a lot of money on providing "universal" public services that are largely used by the wealthy. Examples of note are major public universities, some transportation systems, roads and highways in expensive suburbs, etc. From a redistributionist point of view, the purpose of government is to take money from the rich and give it to the poor, not to spend it on the rich; this would be the worst sort of nanny-state behavior. It would be better to tax the rich (possibly less) for goods specifically intended for the poor, and to let them fund their own roads and hospitals.
3. Inequality and poverty. Poverty matters; inequality per se does not. It's OK for there to be arbitrarily large differences in income and lifestyle as long as (a) no one is starving or is otherwise deprived of necessities, (b) there is some degree of social mobility for the poor (i.e., "equality of opportunity"). In general, wealth and happiness are non-zero-sum; there is usually a trade-off between efficiency and equality of outcome; one should maximize efficiency under the constraint that no one is living in actual poverty.
4. Unilateral military intervention. National sovereignty is stupid and immoral. When one believes that other countries (or cultures) are engaging in abhorrent activities, it is reasonable to invade if one has the power to do so. The United Nations is not a representative world government as it consists largely of dictatorships, the UN Human Rights committees are worse because dictators are disproportionately interested in being on them; in any case, the UN has no legitimacy. In general, rich western governments have at least as much legitimacy (in the normative sense) as the local warlord when it comes to representing the interests of the citizens of, e.g., Sudan or Iraq. [I should note that I still think this is true normatively; however, one must also consider the descriptive sense of legitimacy, and the impact thereon of the fact that occupying troops tend to corrupt over time.]