Since i make long trips (some over 300 days), I've had some experience with this. I ask for 90 day scripts with 4 refills, my insurance allows for one vacation fill per year (also 90 day) so I can leave with up to 180 days of meds. None of my scripts are controlled substances that have 30 day only fills.
The problems? First, up to this year my pharmacy was a small chain with stores only here in the northeast. If you transfer a prescription to a different chain the refills are canceled. By the way, here in NY you may find your refills canceled even if you go to a different physical pharmacy in the same chain. My solution for this problem is to talk my doctors into providing 2 90 day paper scripts (with refills) for each medication that I carry with me. I can use these at pharmacies in what ever state I'm in when I run out of meds. If you are planning a year long trip you should get the paper scripts as close to leaving as possible - they are only good for 1 year.
While I've attempted to have prescriptions that have refills transferred from my local hometown pharmacy to a pharmacy where I was currently located, I've had mixed results. Time zone differences, wait times, etc can be a problem if you are not staying in one location for more than a day or two. Because of this, I have reluctantly changed to a nationwide chain pharmacy. Because they are connected electronically, I have had no problems getting refills anywhere the chain has locations.
Unfortunately, nationwide is not quite nationwide. For example, some states don't have CVS pharmacies, some don't have RiteAid, etc. While there is a Walmart just about everywhere, some don't have pharmacies. Many small towns, particularly in the west only have one chain pharmacy, and the nearest "other" chain pharmacy may be 200 miles away. My insurance lets me do a refill 2 weeks prior to running out of medication, so I start looking for one of my chain pharmacies when I get close. The major chains have on line search pages that are useful for finding locations.
While it is technically possible to have the pharmacy call your doctor for a script, again, time zone problems, long wait times, & explaining the problem to the doctor or nurse makes it difficult.
For those using mail order pharmacies, it solves the refill & local pharmacy problems, but introduces post office general delivery hassles, knowing when & where you will be, etc. I'm also concerned about heat/cold in that one of my eye drops has a fairly narrow range of storage temperatures. Sitting in a Arizona post office might well exceed them.