First, the disclaimer. When I was a pro player I was a member of Philadelphia's Local 77, but lapsed out when I changed careers. However, I now represent unions for a living, as a lawyer, in Los Angeles. I do not work for the musicians union but am generally familiar with their practices and general political direction, at the Local and International (US and Canada) level - and to the extent the AFM (more properly the Film Musicians Secondary Payments Fund) "me-toos" onto residuals collection deals I negotiate for my film-industry clients out of bankruptcies and the like, I'm proud to say that over 20 years, I've helped move some millions onto the musicians' side of the ledger.
What's right for you? It all depends what you aspire to in the way of a career. As others above have noted, if you want to do orchestra/theater pit/recording/high-end touring/high-end corporate/GB gigs, you'll have to be a member. If your skills or aspirations are not at that level, you can probably get away without it.
I'm not familiar with details of current AFM contract provisions (except concerning collection of residuals for film and TV work) but in general, the more you work under union contracts, the more you'll see in the way of pension/health benefits. So even if you can get away without it, you may well be better off working under those contracts whenever possible.
There is no question that some locals are more effective than others, and that there are some where historical practice has featured some degree of self-dealing, nepotism and the like (don't get me started on Local 77, back in the day!) However, I don't see anything different in many corporate or business settings. It's a sad fact that humans often take advantage when they can, and it's particularly jarring to see it in the context of a union movement that is rooted in communitarian and egalitarian ideals, but that's showbiz for you...
Meanwhile, those union contracts provide a floor. Doing society gigs in Philly back in the day, the contractors knew they couldn't get decent players for less than scale. On the road, in settings well above scale, that "floor" function was useful when novel situations arose, such as the first round of concerts being filmed for MTV and other use, back in the late 1970's - early 1980's. Scale for record dates under union contract (would that there had been more of that!) meant not only payment at the time services were rendered, but also an annual payment from the applicable recording fund, collected on an industry-wide basis. If you manage to do union film work, you'll see a royalty stream as well as your initial compensation.
Is this an effective floor? In many ways, no. Consider supply and demand relative to the history of musicians in America. In the '20's every radio station worth a d*** had an orchestra, live theater meant live musicians, and there was lots of work. Mass dissemination of recordings changed that dynamic. Movies with sound changed that dynamic. TV changed that dynamic. Rock and Roll changed that dynamic, as performance opportunities opened up for a much wider range of folks. Changing tastes and budgetary pressures changed that dynamic - no more variety shows on TV with full orchestras, and call for recording musicians on TV has continued to diminish ("Lost" and "The Simpsons" are the only TV shows that come to mind that have used full-sized scoring ensembles, but there might be a few others). Digital has hugely diminished performance and recording opportunities - in the studio, where emulation knocked a lot of string and horn players out of work (that's when I got off the train, as a trombonist, in the mid-'80's) - and live, where society bands can now be skeleton crews playing along with digital rhythm tracks, if they are even working at all because folks instead opt for DJ's at private affairs. And it's all one big spiral, as the less-often people hear live music or non-digital sources, the less they expect in that way. And hey, let's not forget digital piracy, which is putting a hurt on writers and performers in ALL genres. And many producers will always be looking for ways to get their music for less, by trying to get their music via non-union sources.
So in this context, where technology, budgetary pressures and popular tastes conspire to reduce performance opportunities while also expanding the pool of potential performers beyond a small group of people who spent years mastering arcane instruments (to be clear, my point is that one can get to a creative and performance level more quickly in many popular idioms than would have been required in the pre-Rock era), the union is forced to engage in constant rear-guard action, toward preservation and incremental improvement of wages/benefits/working conditions in the remaining sectors where there is demand for exceptionally skilled players. That's the reality. My guess is the high-end work will continue to be organized, but that it will be an uphill fight to expand the use of AFM contracts over time. And it's interesting to see that the AFM now has International leadership drawn largely from the recording community - those folks will be working hard to redress some ways in which they've been taken advantage of or have been taken for granted by past administrations, but as they head into the future they will also have to consider the prospects of their co-unionists that are less-skilled, less-fortunate, not living in cities hosting genuine recording activity, or deeply committed to less-remunerative forms of music-making.
So what does this mean for you? Again, if you want to do high-end work, you'll join. If you want to be around folks who do that work, joining can provide benefits - like the fellow above who used the rehearsal bands at Los Angeles Local 47 as a job referral service. If you lurk behind the union contract but don't join, you'll periodically free-ride on the wage floor set by those contracts, but you won't have the pension and health angle covered, or participate in the special payments funds. If you don't think much of the way in which your local is run, you're likely not the only one with that opinion, but the only way those things change is if you and others get together, get involved, and make change happen...as happened at the last International convention, with a sea-change in leadership that evolved from the work of many union activists, over many years.
One last bit - the question of unions in America is highly politicized. Unions brought you the weekend, wage-hour laws, and a host of other benefits we all now take for granted. One can easily argue that no country (other than Japan?) has enjoyed a stable and prosperous middle class without the efforts of a union movement. On the other hand, unions aren't perfect, and in many ways they cannot transcend the limits imposed by mismanagement (Detroit!) or general economic conditions, and unionism is often cast as a "blue-state" phenomenon, which is astounding when you consider the complete history of unions in America. But in thinking this through, try to put all of that aside and take a look at the costs of membership (initiation and dues) as compared with the benefits FOR YOU, in your current and aspirational work contexts.
Stated simply: who do you want to be?
Best of luck.