Answer:
It's hard to know exactly but we have a pretty good idea. These numbers could be off by two or three in each category and some emperors deaths are unclear.
I will do the short version. To clarify, visit Wikipedia on the subject. It has a pretty concise list.
Total number of emperors, from the first one in 63 BC to the last one there were
Total = 91 (approx)
(I say approximately because at times, there were co-emperors, usually a father and child duo)
Emperors assassinated or murdered or executed (either by individuals, groups of senators, guards, poisoned by their wives, or had legions of their own army turn on them)
Total = 33
Emperors killed in battle (or captured and executed by their captors or died in captivity of other [natural] causes.
Total = 12 (approx)
(again, there are some circumstances that are unclear exactly what happened)
Emperors committing suicide
Total = 6 (approx)
Emperors who went insane and died shortly after
Total = 1 (confirmed)
I think it's worth mentioning some of the methods of assassination: strangulation, poison, sword/knife, stoning, quartered (all 4 limbs tied to 4 horses and torn apart) and beaten to death by mob and I'm sure there might be some I'm missing.
Lastly, unless otherwise specified, all others died of natural causes but it might be worth mentioning that there were a few peculiar deaths which would be considered natural causes: one death by lightning strike and one by suffocating on fumes from being trapped in a fire during battle.