The problem with a one-dimensional compass is that in the world of liberal vs conservative (an economic scale), there is an awfully large overlap between the extremes; Greens and Libertarians have a LOT in common. The only explanation is that there is another metric. Enter the social scale, weighing personal freedoms of the individual (the lowercase-l "libertarianism" or "personal") against the united power of government ("authoritarianism" or perhaps "statism"). Greens are personal liberals, Libertarians are personal conservatives. This two-dimensional compass was pioneered by David Nolan (a Libertarian Party member) and is formally called a Nolan Chart in his name.
I've done a lot of toying with this concept lately. There are three main implementations: the quick-and-dirty World's Smallest Political Quiz, which heavily favors the US Libertarian Party (it was written by Nolan and his advocates), derivate project VoteMatch, which tries to remove that favoritism and further matches your scores to prominent politicians, and The Political Compass, which is less biased and has more clear labels.
World's Smallest Political Quiz
This mapping uses two dimensions, economic (liberal vs conservative) and social ("populist" vs "libertarian"). I dislike both of the terms used on the social scale, and the fact that the scale ignores the fact that each pairing should result in a pairing of the labels. This is one of the key criticisms noted in the WikiPedia article.
Putting the dimensions together with one's score results in a nicely rendered mapping with only one label despite that each label refers to only one of the axes. For example, you might score low on both scales, which would label you "populist" despite that you are also liberal (perhaps even more so!). Worse, the term "libertarian" has two meanings; the (capital-L) Libertarian Party (US) is right-leaning in its nature, even though the term "libertarian" really only indicates a social leaning. This makes it a bad label for this test. I advocate for "personal" instead. I'd call the other direction (low on the social scale) "nationalist" instead (other tests call it "authoritarian" or "statist").
The bias of this test is clear; they've manipulated the test so that it favors higher scores on both scales, and they also utilize the psychological instrument of "higher is better" to put (capital-L) Libertarians at the "top."
I found two incarnations of this test, both of which appear to be maintained by ontheissues.org. One of them crashes for me, so I linked the other. Please note that the linked speakout version reverses question 14, which should be "decrease overall taxation of the wealthy."
This test suffers the same labeling problem of The World's Smallest Political Quiz, which will hopefully be fixed along with the aforementioned bug. The main merit of this site is that it allows you to compare your results with the computed results of various politicians, giving detailed explanations of each issue, boiling right down to the politicians' voting and campaigning records. This is a hell of a merit, and kudos to this team.
Note: more than the others, this test is mostly only applicable to present-day politics in the United States. (Since the "politics" category isn't available to journals, I chose "United States"
The Political Compass
This test differs from the above in that the scale is flipped vertically and rotated 45 clockwise. It is properly labeled. The only issues I have with it are the positioning of Mike Gravel on the US Primaries 2008 page, which is clearly biased by his new political party (Libertarian) rather than his platform or history, and more seriously, question 2 on page 4 of the quiz is ambiguous and should state "it is preferable to have a one-party state because it avoids
all the arguments that delay progress in a democratic political system" rather than "a significant advantage of a one-party state is that it avoids
Because of its proper labeling, the final paragraph of WikiPedia's criticism section does not apply. Its axes aren't biased to favor the Libertarian Party, either (if "higher is better," then it favors Neo-cons). However, I still think the term "libertarian" is misleading, and I'd prefer the social scale to compare "personal" to "nationalist." The explanation bit has some fine print that uses even better labels, though they're too verbose for category titles: "voluntary regional collectivism" (personal/libertarian) vs "state-imposed collectivism" (nationalist/authoritarian).