It depends; I don’t know what sort of rig you have. I’ve been to Yellowstone numerous times and have never made reservations. Only twice have I not gotten a spot, even in prime time. Once I boondocked outside the park and got a site in the morning. The other time I had to take a spot in Fishing Bridge for a night, a real downer to me. But I have a 16’ TT and can get into almost every cg in the park; a large unit wouldn’t have that flexibility.
I almost never make reservations; it’s incompatible with my wandering type of travel. Only if I’m near an urban area and there’s no public land will I do that. When I know where I’ll be in the evening the DW calls ahead and finds a spot and we’ve never failed to get one.
There’s a lot of public land in the west and if you’re amiable to boondocking you’ll have a lot of options there. Then there are parking lots, something I’ve never done but it might work in a pinch. gbopp’s links for free camping would be another good source and there are a couple of books out that list free campgrounds across the country that would be a good resource. There are 2 volumes, one for the east and one for the west and I’d guess they’re probably $15-$20 apiece. Sorry I can’t recall the titles but it shouldn’t be hard to track them down.
If you’re uneasy about not having a reserved spot and maybe having to wing it, or if you have a bigger rig, reservations may be the best idea for the parks. I think, though, that on the trip itself you’ll do fine just calling ahead to various cg’s when you know about where you’ll be. Not having reservations is unnerving to some, but I think the freedom of not having your day dictated by a schedule far outweighs any downside. Have a great trip.