Fear of being left- Check! Done that one, and still working through all the ramifications of those transitions in my life. While it's not exclusive to poly, life is a numbers game, and if you have more partners, chances are good that at some point, someone is going to opt out. Does the world end? No, but it can sure feel that way at times.
Fear of being open- Check! When there is pain from a variety of sources, extreme stresses, it may seem like a better idea to batten down the hatches and keep your cards close to your vest. If I'm closed-off, there is no way for anyone to become close, or stay intimate though. This can be a compounding fear. When no one can get close, it's the same functionally as pushing people away, and they leave. Staying open in the face of fear is one of the biggest drains on personal courage I have experienced.
Fear of not being picked- Check! We're out there reaching for someone, and they don't reach back. Hard. It gets harder when they reach towards someone else instead. Why not me? It brings up all those childhood issues about being picked up for teams, and being the last one standing. This is something regularly dramatized in popular culture: Kids lined up on a playground: the hopeful look fading to desperation, then desolation, and often self-loathing. What it comes down to is that I can't control the desires of others, and need to stay resilient, not putting many eggs into a particular basket until it looks like reciprocation is likely.
Fear of rejection- Check! This is a little different than being left, happening earlier in the course of a relationship. Someone gets to know you, things start to move into the direction of importance, and then, they hit on something that doesn't work for them, and opt out. At this point, it really is me, or at least me bumping up against them. It's a big world out there, and a lot of options to explore. Not everyone is going to like my chips. A few will sample and move on. Others will come back for a steady diet. The chips are still quality, but some aren't fans of salt 'n vinegar. ;)
Fear of being wrong- Check! The adjunct of this one is "fear of making a fool of myself". There are so many opportunities for miscommunication, sometimes leading to poor decision-making, deciding to go farther out on a limb emotionally than there is tree to support, to set down a "rule" and then find it does the opposite of the intent, to have the "stupid pink fuzzies" of NRE so severely that it damages existing relationships, to have baggage from the past cloud future perspective, and a host of other exciting possibilities that are often blundered into without awareness.
For this one, I just flat out accept that I WILL MAKE MISTAKES. I WILL BE WRONG! Some of those mistakes won't be recoverable either. I regularly practice apologizing to others, and try to be clear with my partners that I don't have all the answers, that I mess up, and to encourage them to call me on it when something seems off, preferably before it's a significant problem.
Fear of taking too much on- Check! I strive to give quality to each and every person that is important in my life, and there have been times where I've bitten off more than I could comfortably chew, to the detriment of myself, my family, my business, and/or a partner. Getting to know my bandwidth has been a process of trial and error. There have been times where I've had to back away from a connection that seemed promising because there wasn't anything else that I was willing to take time or energy away from. As life circumstances change, bandwidth adjusts, so this is an on-going project, to be aware of what I have to give.
Fear of being too shiny- Check! There are times where I've entered a relationship with someone, and they are significantly more "into" me than the inverse. This creates an imbalance in power that feels really uncomfortable to me. Assessing how well someone manages relationship expectations is part of my screening process now, as is communicating how deeply emotionally interested I am. If there is pressure to always give more than I have time or desire to invest, it's a big red flag for me.
Well, that's a starting point, but certainly not a comprehensive list! What are some of the fears that you've bumped up against in your exploration of poly?