You'll find that this forum has folks who hate to reserve ahead, prefer the freedom to change plans...and others (like me) who enjoy the process of mapping out every tiny detail in advance. Most fall somewhere in the middle.
I like to book online and have a printed confirmation, but you can pick up the phone at lunchtime and give them a credit card for that night. Or just show up by 6 p.m. or so. Some places even post signs after the office is closed telling you to pick a site and pay in the morning.
Pay attention to cancellation fees even if they don't mention on the phone (ask) before giving a cc, just in case. Some places have hefty canx fees, others have none.
Whether or not you need reservations varies by where and when, all of us might agree.
Resort/heavily touristed area in high season, probably.
Weekends and holidays, good idea to reserve ahead or at least call a day or two out.
High demand and low price (state park on the water in Florida Keys, for example), almost impossible to GET a reservation the minute the booking window opens), though you can always show up and ask.
Off season when kids are back in school, reservations generally not needed, unless there's an event like the Albuquerque Balloon Fiesta.
Mid-afternoon at a place along the interstate is usually easy enough to get because they cater to over nighters.
There are some handy apps like Allstays Camp & RV that can locate campgrounds.