Perhaps to ask a follow up, how did passports work before the nation-state? I know that Austria-Hungary had an Austrian passport and a Hungarian one, but I don't believe that's how it worked in the Holy Roman Empire.
I think you need to think differently about travel and borders in the 17th century. Remember that the National State, as we know it today, did not come to existance before the 19th century. My field of expertice is travel in the late middle ages, but concidering how the concept of states did not change much until the 19th century, I might be able to give you some input on how it might have been.
First, travel in the middle ages, or early modern times, was not usually done for the sake of travel. The first man who is believed to have travelled for the sake of travel is Ludovico di Varthema in the beginning of the 16th century. So, here we obviously have a difference between the middle ages and the early modern times. Although, most would not have been free travelling men. Mostly because it was a dangerous affair.
Now, this takes me to my second point, which may begin to answer your question. The dangers of travel may have been a way of telling whether or not you were still in your state. Moving between states was to move between jurisdictions with different authorities. In the 17th century, you'd also sometimes move between states with different religions (protestant, catholic, and even islamic).
Since you ask specifically about HRE in the 17th century, I'd say that is a difficult case. I've now given you different points of reference for a traveller to orient himself to where he might be (jurisdiction, authority, religion). Now, within HRE you'd have states that separate each other in the same way that France and Austria separated each other (language is not a good marker either, considering all the different languages in Austria or Spain).
Third, all these things considered, vagabonds was widely persecuted in many states. In the middle ages there were a few reasons to travel; pilgrimage, missions, diplomacy, study, commerce and war. And to not be mistaken for being a vagabond, you'd most likely have to get permission from the states authority (count, duke ... ect) to travel through the land.
In conclucion: nations weren't nations at that time, and it would be hard to travel freely since you could be mistaken for a vagabond. There wouldn't be an obvious border to cross, and you'd most likely have to seek the state authority to travel further through the land. Knowing that you were in a different state was probably a slow process compared to how we think of it today.
This might have been a bit speculative, but I hope it may have helped you to paint a picture. And remember; my answer is based on the presumption that 17th century Europe had much of the same "border controll" that 14th century Europe had. I know that there are some obvious differences (like; standing armies, absolute monarchy ... etc), but I'm not sure if the free travelling man would have noticed much of that. I'm happy to be corrected if I'm wrong.
litterature for further reading: Ohler, Norbert (1995) The Medieval Traveller. Translated form german by Caroline Hillier. Woodbridge. Pp. 1 – 220. Phillips, Kim M. (2014) Before Orientalism. Philadeliphia. Total Pages: 304.