Not unlike many people around me, judging others and their actions is something I do quite a bit - sometimes subconsciously, but many a time this also happens when I'm quite aware of it. Now I know of course that being judgmental is not a trait we look upon with great admiration -- but nobody can deny that some judging from time to time is pretty good for a laugh.
There is one school of thought that argued for the suspension of judgment: Pyrrhonian Skepticism. This is mostly advocated through Sextus Empiricus, who probably lived sometime in the second or third century CE (history is a bit vague here). This particular strand of skepticism is interesting, because it is not so much the content of the philosophy that makes it intriguing, but rather its attitude towards philosophical problems.
Sextus Empiricus, along the lines of Pyrrhonism, argues that as a Skeptic we can never decisively and definitively say that one account or opinion or judgment is better than another, so we should therefore suspense our judgment. A Pyrrhonian Skeptic, however, is not someone who gives up on learning or stops seeking arguments for both sides, but someone who accepts that if she does not have enough knowledge or arguments to say "A is right, and B is wrong", she decides to suspend judgment until she does. But that's the trick: she is convinced that she will never have enough knowledge to make a judgment, so she will always suspend it.
But why should we in turn be convinced by the Pyrrhonian Skeptic? According to Sextus Empiricus, suspension of judgment takes away the trouble of daily life, at the root of our unhappiness: the trouble of trying to decide what is the best judgment* to make. If you do not trouble yourself with this seeking for the right answer, this will lead to tranquility** which is the goal of (a happy) life to the Skeptics.
As with every philosophical school of thought, there are critics. One that I find most notable is offered by Myles Burnyeat, who points out that in order to be convinced that suspending judgment is the way to go, it is inevitable that you judge that there can no investigation will ever produce a convincing answer... How to solve this contradiction? Advocates of Pyrrhonian Skepticism would say, that it never meant to say that it is convinced that there are no convincing answers, but simply that it never saw any evidence to believe that there are convincing answers.
Even though I will never (be able to) lead my life without judgments, perhaps this should inspire me to at least try to suspend judgments sometimes, for example when this woman on the train is breathing so loudly it makes my blood boil. Perhaps some tranquility wouldn't hurt sometimes. Are you convinced by the Skeptic argument? Do you see a way out of Burnyeat's criticism, or is this Skepticism inherently contradictory?
*This leads to trouble in the mind of the Skeptic: because there is no "better judgment", and thus you spend your life looking for something that does not exist.
**In Greek: Ataraxia
To go with Sextus, I would advise a lovely "Pierre Jourdan Tranquille" from South Africa. Next time when you have a heavy breather on the seat next to you, just relax. Take a sip, take a breath. No judgment.