I just noticed the following words from arXiv:
"You are encouraged to associate your ORCID with your arXiv account. ORCID iDs are standard, persistent identifiers for research authors. ORCID iDs will gradually supersede the role of the arXiv author identifier."
I thus wonder if a person's profile in ORCID is really that important, given that the person would like to pursue a career in academia?
While I largely agree with Ian's answer (ORCID might matter in the future, but doesn't right now), I see one place where it may already matter and a reason why it should come to matter more in the future.
Right now, there is a strong implicit presumption of the uniqueness of a scientist's name, and all of the literature searches and citation databases, etc, of the world get rather confused when you have a person who either a) shares the same name as other practicing scientists or b) has a name that changes over time (e.g., marriage, gender identity change) or is represented differently (e.g., transliterated) in different papers.
On this site, we have a number of good, difficult questions dealing with the problems that name change and transliteration cause, which is particularly acute for academics in countries that don't use the Latin alphabet (e.g. this excellent question). These problems will grow in importance as the number of practicing scientists grows and becomes more diverse, and as the duration of the readily searchable literature grows as well.
In short: there is a rapidly growing need for something like ORCID that makes it easy to distinguish scientists without context-sensitive text mining. Whether ORCID is that thing, and how long it will take for it to be widely adopted and effective, are both open questions.
My personal opinion is that right now ORCID has pretty much zero traction in academia: when my university partnered with ORCID and pushed uptake quite hard internally (by its standards, at least) I was the only person in my department who'd even heard of it (whilst nearly all knew of, and used, the arXiv).
I think it likely that ORCID take up will increase, but in the short term it's of no importance at all.
Update: Here is a JISC report on the trial implementation of ORCID at a number of UK HEIs, including my own. It lists a number of benefits (the key ones covered in @jakebeal 's answer), but more importantly illustrates the high level (research council etc) support for ORCID. With my sceptical hat on I will note that I couldn't find numbers as to how many new ORCID IDs were generated by this pilot.
Let me count how many academic IDs I have:
They never agree on the counts of my citations, of course, or even on the number of published works, even though some of them cross-link to one another.
Google, Scopus and Microsoft are, of course, automatic. ORCID, ResearchGate, RePEc, ResearcherID require registration. I don't have arXiv ID; I've never been able to extract value from that service, and at the time I bothered about these IDs, it was purely mathematical, which did not quite ignite me, and it failed to compile my LaTeX code because I had graphs in my papers that exceeded the then-existing file size limits (something like 1 or 2Mb in early to mid 2000s?). I am sure I am missing another five or so academic ID services. I remember starting some of them, but never being able to populate them properly, because they said something like: "Oh, just push this button, and we'll search ISI WebOfKnowledge for you" -- guess what, they don't do it on their end, they do it on your browser, so you need to have access to ISI for that stuff to work.
Does missing any one of these services matter? This is probably discipline-specific; I would venture a guess that nobody in this thread heard of RePEc (REsearch Papers in EConomics)... but if you talked to economists, they probably would not have heard of ORCID in return. Given that you are coming from arXiv, you are probably a mathematician or a physicist, and arXiv is probably the default for these disciplines, with little to no need for other IDs. That is to say, if you only care about becoming a famous physicist through publications, stick with arXiv ID; if you want to be a good citizen of academia, so that other academics sort of recognize you when you step out of the door of your home department, or if you reasonably expect to collaborate with other disciplines, ORCID will probably help.
Coming back to the OP question, my specific suggestion would be to check what people put on top of their CVs in your discipline/in the departments where you are looking for a job. If it is an ORCID, you need to get one. If it is an arXiv ID, you need to get one. If it is a picture of their chihuahua, you... well, you get the drift. (My scanning of CVs in a discipline that has a sort of dual identity, sociology, when I was interviewed by a sociology department years ago, revealed that some of the faculty think of themselves as scholars, and list their published works under Scholarship, with these works being books or chapters in books, with few to no papers -- these would be doing sociology theory or some social forces or stuff like that; while others would refer to themselves as researchers, and list their published works as Research, which would consist, for the most part, of journal papers, which would be more likely to use quantitative methods. I don't know much about sociology, but I imagine there are internal tensions between these groups, with one not understanding the approaches and achievements of the other.)
NSF has just thrown out it's CV/resume system for grant proposals and adopted ScienCV (NIH's sysetm), roughly speaking. This system can, with a fair amount of work, mine your ORCID and setup your CV for NSF's grant proposals for the future. If you submit a proposal without using this "new" system, NSF will return it without review. ORCID is probably the easiest way to construct what NSF and NIH want in ScienCV, though I haven't completed mine yet (I've barely started it).
ORCID may never take off as a universal system for finding researchers and their latest publications, but US researchers who want to keep their jobs will be forced to keep theirs sort of up to date so that the granting agencies at the federal level can see them and use them for review. Whatever ORCID does, it still suffers from an/the updating problem.
