TIP: Don't take something to the store upon first crash.
I had "put up" with the crashes for a long time. Patience is a virtue, although waiting until your warranty is up is not good. In this case, I had experienced enough crashes across enough updates to indicate the problem might not be the OS itself. Unless your Mac or iPhone is clearly broken, try searching for your issue on the Apple discussion boards and search the support docs for troubleshooting tips. Some basic troubleshooting tips usually include: rebooting, uninstalling/reinstalling, setting up a Guest user account (on Macs) or restoring your iPhone to factory settings.
TIP: See what conditions cause the issue to occur and document or explain those to the Genius.
In my case I "restored" my iPhone (a clever euphemism Apple uses to hide the true meaning: nuke your device back to factory settings) and tried starting from scratch. My frequent crashes and disconnects from iTunes while syncing indicated a hardware issue if the OS wasn't corrupted. So I had to eliminate the OS as a cause by re-installing it.
The problem was, as a factory-fresh install, the iPhone worked fine. So I started adding only content, not apps. Music and videos starting eating up the gigabytes and, sure enough, things started to go horribly wrong. I was able to reproduce the issue only when the device was filled with more than 2GB of data, it seemed. This indicated it was not the sync cable (I had tried several anyway), but possibly the memory in the unit itself.
TIP: Bring any supporting materials with you (error reports, logs, etc.) and explain each issue in detail.
I had the luxury of using Xcode to peep my iPhone's crash logs. You can find these for your Mac in Applications > Utilities > Console, but they are essentially hidden for users on the iPhone unless you are a developer. My crash logs indicated something very, very wrong: the backup tool that runs each time you sync with iTunes was bombing in a bad way, as though I had ripped out the iPhone in the middle of a sync. That again indicated (to me) that there was a bad block of memory somewhere. When the Mac tried to read or write from that block, the OS just freaked out and crashed.
TIP: Try it twice.
I tried restoring my iPhone twice just to make sure I didn't get another corrupted install. It amazes me how computers screw this up, given that they are supposed to be famous for doing the same thing given the same set of instructions, but "things happen" as they say -- give whatever you're doing two chances to make it right. Three strikes if you are generous and have the time. Personally, it was a huge enough pain losing all my preferences and settings and game data the first two times. I felt I had enough info at this point to march into the store with a Genius Bar appointment....
The Genius at my store was impressed with the level of detail I was able to go into, and as a result he was able to simply confirm my findings and provide me with a new phone. It took longer to charge the device (which had been sitting in a drawer for a while) than it did to diagnose.
Be patient, be aware, come prepared -- do those things and your unfortunate trip to the Genius Bar may not be in vain.