What would Soviet History have been like if Trotsky had not been murdered, do you think?

I think it would have been the same. Trotsky was way out of the system and hiding/working in Mexico when he was killed. He had little influence over Russian politics and I believe he would have continued to have little influence - he wasn't a threat when he was assassinated. I think the question should be, 'how different would Soviet History be if Trotsky hadn't been forced out of the Soviet Union?'

As Redrum said, it wouldn't have been much different as he was already exiled (of sorts) in Mexico. However, he was causing a lot of mischief abroad, enough to warrant his removal, so clearly, had he been allowed to live out his days, he would have amassed a much greater group of followers.

If he had managed (rightfully) to gain power after Lenin's death, instead of Stalin, then speculation runs wild. We must remember that the party that put Marx's writings into action, and spawned (or influenced greatly) all of the quasi-socialist totalitarian regimes that the American government has hated and continues to hate, was the most pragmatic and extremist socialist/communist party in Russia at the time, and its extremist nature is the reason why it succeeded. Trotsky was willingly part of that group, and indeed was a mighty military strategist (he developed the line of machine-gunners who fired on deserters - although this needn't be viewed as so brutal when taken into consideration that countries like Britain sentenced deserters by hanging well into WWII). However, Trotsky had qualms with even Lenin's excesses, which were nothing compared to what Stalin concocted, and he wanted a democratic framework. Looking back now, we can see that socialism would have worked a lot better with democracy (as limited as it may have been). I imagine that, after the country was stabilised, he would have taken on more of an advisory role, in contrast to the dictator-like role that Stalin took.