Yes, they do. Just like parishes.
Because you advised the OP to do likewise. That’s the problem. You as much as told the OP to just pick a parish and consider himself a member there–without any regard for what is actually written in canon law (in fact, you implied that canon law says it doesn’t matter), and without any knowledge of the OP’s own situation. You based your answer on your own anecdotal experience of registration, rather than on what the universal canon law of the Church says with regard to parish membership.
It’s not a violation of canon law to register at a parish other than the parish where you actually live because there is no such thing as parish registration in canon law–there is parish membership, not parish registration.
Now you have me totally bewildered. The OP never asked what parish he’s a member of. He asked what the advantages were to registering anywhere at all. Now you say registration means nothing in the end, anyway, which in some dioceses isn’t true when it comes to marriage or burial outside your territorial parish, sending your kids to school at a parish outside your territorial parish, and, let’s face it, pretty much anything else you ever actually do at a parish, other than your territorial parish.
OP here. I attended my territorial parish for Sunday service. It seemed nice.
A good summary. I could add that registering in a parish seems to be an American preoccupation. It is not the practice here in the UK, for instance, apart from when wanting to take part in a donations scheme.
Right.
That second paragraph is the problem. All diocese DO enforce parish territories–this isn’t something where bishops just have the option to follow canon law or not follow it (which is what has been implied).
Yet when OP included in a recent post, “Another parish may provide the services if registered and/or allowed by the diocese”, you responded “right” to OP’s post. 
If I wrote that, I did not mean that, at least not in the way I am reading you to say. I think I’m not expressing myself well at all, here.
I know you were referring to anonymous donations to one’s territorial parish. But I recently learned of a case in the territorial parish for Catholics in my neighborhood where the priest refused to baptize the child of parents who attend there because they do not use envelopes. It is not their territorial but they are registered there.
I’m not sure how you would go about unregistering. I suppose just inform the parish that you no longer want to be on their registration rolls. Or perhaps following a period of no donations or participation, they will simply remove you on their own. In my original home parish, I eventually no longer appeared on their member roster.Firstly, everyone I ask says I don’t HAVE to register with the parish closest to me geographically.
Also, how do I “unregister” with a parish. WHat is the correct way to do this?
My guess would be you can register anywhere then as one would hope the deacon was aware of the policy. But if you question whether he is, you could make a call or shoot an email to the diocese. Where I live (not in MN) I emailed the diocese and received a response that there was no official diocean policy here. That it’s up to individual priests if they allow folks who live outside of their parish to register in them. I then called a couple of parishes and both do.
So if I understand the aspect of the canon law being discussed,
However I just learned further that the proper parish for Catholics in my neighborhood will not even baptize a child of members unless the parents are registered and use envelopes for 6 mos.