To jump in the most recent of conversations:
Most of our people have tsuba, but you should be able to eventually receive a technique and absorb to the point that one isn't necessary. I am nowhere near that and I am more than thankful that I have one. My knuckles sometimes still get bruised, even with a tsuba because the bokken comes over the tsuba as they continue to cut down as I lower my hands to receive. My old dojo used to encourage me to "go for it" and I would have been a lot more hesitant to have done so if I my partner didn't have a tsuba or if I wasn't confident that they could take care of themselves.
Here is a link to two guys at Birankai Summer Camp demonstrating kumitachi: http://www.youtube.com/watch?v=e_k0m...eature=related
Though these two have tsuba, Birankai doesn't necessarily endorse one way or another. Tsuba or no tsuba, I don't care. I want one; what you have is up to you. Just be prepared to take care of yourself. Traditionally speaking, I have never seen a shinken without a tsuba though.
To answer the original poster "Does anyone know why aikidoka typically train with bokken that have no tsuba? Are there styles/schools within aikido that typically do train with a tsuba? Has anyone trained both ways and has an opinion on which way you prefer and why?":
My dojo mainly uses tsuba, but there are a couple people who do not. I have trained with people who prefer no tsuba. Some is personal preference, some is dojo preference and some is more of a stylistic preference that is passed down from their teacher's teacher. The easiest way to answer your question is the reason your teacher does it that way is because their teacher did it that way and their teacher did it that way... It also depends on if your dojo in particular has a heavy influence of iaido or anything like that. Those dojo's may or may not prefer tsuba for that reason.