I only have experience with Romance languages (other than English, my native language) and you can NEVER split your infinitives. Hablar in Spanish could never be split into two separate words as in "to talk" like we do in English.
My question is, are there other languages that split infinitives into "to" and then the verb (or something similar) other than English?
Regarding Romance languages, yes it exists! In Romanian (a Romance language) the infinitive is formed, as in Norwegian!, with adding "a" in front of the verb form:
to study = a studia
to drink = a bea
In Hebrew (ancient and modern) the "ל" is attached in front of the word (as many other prefixes) which in my mind is the same as having two different words... This is so, since the prefix is not inflected.
Most important is to keep in mind that the English Infinitive is not equivalent to 'those' in other languages and/or other languages don't have the infinitive at all. Greek (Ancient and Modern) are two such examples...
NOTE: edited to clarify that Greek (Ancient and Modern) are two languages. Thanks slogger!
BTW, according to some sources, English does not always use the "to" to express the infinitive. For example, the "eat" in "You may eat all day!" is considered the infinitive form.
Apparently, it was a Victorian rule, to not split the infinitive. It was acceptable 800 years ago, and is commonly done nowadays.