Are there any crimes in any state that do not come with the option of probation?

The answer to your question is that there are many crimes that probation is not an option.  They are crimes with mandatory minimum sentences.  For instance, a conviction for criminal domestic violence 2nd Offense in South Carolina carries a mandatory sentence of at least 30 days.  There can be probation after that, but a person with that conviction must serve at least 30 days.  I suspect all states have some crimes that have mandatory minimum sentences, but you would need to check each state and each crime to know for sure.