Well, let me share my experience then:
I worked for a non-union (that is, no contract) scheduled carrier between 2008 and 2010. The Teamsters were on property at the time, but they were so very useless that their presence wasn't even considered by most pilots. There was no union protection, and no appreciable union membership. For all intents and purposes, it was a non-union airline "represented" (to use the term loosely) by IBT Local 747.
For the first year I worked there, management and the pilots had a good working relationship. If you needed management's help, they'd help you. For example, during initial training I was told that I'd be based in SJU, and that I should start looking for an apartment. I set up living arrangements with two other pilots in preparation for the move. About a week before training finished, however, the new system bid came out; I couldn't hold SJU. I don't recall where the bid had me going, but it would have required a complete change in plans, not to mention leaving the other two pilots high and dry. Without me even asking, the ACP called me and told me they'd create a reserve line for me down there; after all, they wanted to keep their word.
For the next year or so, I wrote airplanes up, refused airplanes, called in sick, called in fatigued, told dispatch to pound sand, you name it. I never once received a phone call challenging my decisions. The only phone call I ever received was after I had a door come open on approach, a situation that required the FAA to be notified. I never had to speak to the FAA personally; the company went to bat for me and stood in as a buffer between me and the feds. I didn't get so much as a letter about it. The ramper who closed the door was re-trained, and life went on.
In late 2008, there was a bit of a shakeup. IBT Local 747 collapsed (I'm pretty sure a couple of those guys got indicted), and by way of a bit of certification/decertification drama surrounding an in-house union, IBT Local 1224 came onto property. Mediated negotiations started with full force. I was generally in-favor of this, even though I was wary about the idea that a strong union would create a better working environment. As it turns out, my wariness was justified: Within 6 months, the company didn't resemble the same one I'd started at just a year and a half prior. It had, for all intents and purposes, become just like "every other airline." Management/labor relations were strained, the company wouldn't work with you if you needed help, and the pilot group's morale and productivity fell as a result. Trying to make the best of it, I volunteered on the Safety/Training Committee. I enjoyed my role and got to mentor some newer pilots in the process, but it didn't stop the downhill slide. When I left, I was convinced (and still am) that unionization destroyed the good-will working relationship between the pilots and management.
Now, fast forward just a bit (and guys, I have to be very careful here with what I say): I'm at a different company, but management/labor relations are not good. I don't think they've ever been what they were like in my first example. While the union does things every so often that I don't like, I think they're doing a good job overall, and I do feel they're making a positive difference. I'd go into more detail, but you understand if I can't/shouldn't. PM me if you care to hear more of the details.
My point in this entire thread is that you should make a personal decision before you hand off 2% of your paycheck; don't just toe the union line because they show up your first week and buy you pizza or sandwiches. While there are a few people in this thread who have had very bad non-union experiences, non-union companies do exist that treat their employees well.
If you're new to the industry or on the fence, please just think for yourself and don't necessarily listen to the schtick. That is all.