I've been lucky- all of my training partners have been great. However, I do occasionally get questions about annoying training partners. Specifically, how do you gracefully get rid of them. Here are some approaches:
Method One: Be direct: Simply tell them “I don't want to run with you anymore. You annoy the shit out of me.” If you want to make it more dramatic, add something like “Remember on our last run when you talked nonstop for six hours about how barefoot running changed your life? I spent the entire time contemplating the pros and cons of murder versus suicide.” This is probably the healthiest approach and the only one I'd recommend. Maybe skip that last part.
Method Two: Be passive aggressive: This rarely works and is totally unhealthy, but some people find it fun. Start by showing up 15 minutes late to every run. Next, escalate it by having them run first on trails thought wooded areas so they hit all the spider webs spanning across the trail. When running side-by-side, most of us like to run on one side or the other. Figure out their preference then always run on the opposite side. If they duck off the trail to relieve themselves, tell them you'll be the lookout. Look the other way when another runner approaches so they're caught in a compromising position. Finally, invite them to a Mexican restaurant the night before a long run. Insist on ordering a bean-heavy dish. The next day, mix up the anti-diarrhea medication with a laxative, tell them you'll bring the toilet paper on the run, then conveniently forget it at home.
Method Three: Out-annoy them: The idea is to escalate every annoying thing they say. For example, if they say “I'm a Republican and I believe we should have guns!” You respond with “Damn right we should have guns! How else are we going to launch the revolution? In fact, we're having a meeting tomorrow night, you're just the kind of person we're looking for! By the way, what's your blood type?”