The technique of centering the tire bead in the depression in the middle of the rim is essential, always. This guy is pretty chatty but I used this video on the wheel assembly portion of my '
how to build an ebike' series because he does the impossible in real time, right in front of you, without tools. A word of warning though: Significant hand strength is a requirement.
That problem is rare, but happens sometimes, mostly with balloon tires.
Nowadays, with tubeless-centric rims, its the norm. The damn things are actually built specifically to do this. I have some wheels - in particular my Surly My Other Brother Darryl rims that came stock with my Big Fat Dummy - that are so bad I send them to my LBS to swap tires when the time comes. In fact on that bike that is the sole reason I decided to do a second wheelset, because I knew it would be impossible to do a roadside repair with them. My LBS concurred and said they were the most difficult wheels they'd ever worked with.
The DT Swiss FR 560 downhill rim is another one. I've had to give up on some tire combos with it. Tubed tires in particular on wheels like this have less flexible or even wire beads and they are just NOT happy at all with a rim designed specifically to effectively stretch a tire tight over them. Thankfully, my Apostate has these wheels and I have found two tires (Schwalbe Pickup tubed, and Maxxis Aggressor tubeless) that will fit on them. On my new Bullitt I was able to seat a Marathon Plus Tour on one.
Since my original post in this thread, I have found the tools that let you work on rims like the FR560 without losing fingernails, skin and dollars fed to the swear jar.
The unfortunately-named Bead Bro gives you the third hand you've always needed and is a minor miracle worker. And it is such a miracle that the manufacturer commands $30 for one of them. Its worth the money.
And since thats not bad enough, the same manufacturer sells the Bead Dropper lever, which is not indestructible, based on the Amazon reviews, but is ergonomically the best tire lever I have ever used. I can get a great grip on it, it delivers force the best and the damn thing just plain fits in that tight spot very well.
yes thats right another $20. If you are working with tires frequently thats when the money starts making more sense. I am three wheelsets into the Bead Bro and I knew it was worth the money after the first wheel.