We don't travel at peak times and have had poor luck with walkups. We just got back from going the second week in October and watched people getting turned away from Teppanyaki (at 5:00, no walk ins available all evening), the Ohana's character breakfast, Le Cellier and Boma. Some people have great luck with walk ups. I always schedule one sit down meal per day via PS - if I don't want it, we can just not show. But by 4:00pm, I'm always looking forward to a nice sit down hour long dinner with a drink and a waitress - plenty of time to make it to a 6:00 PS.
It does depend on how large your party is - two is easier to seat than six. When you go - September can be easier than Christmas (although sometimes the restaurants are lightly staffed in September and won't seat every table), when you eat - eating a late lunch or early dinner is better than trying to get seated at 6:00. Where you are interested in eating (Marrakesh in Epcot is a great place to go for walkups, Teppanyaki a horrible place to try and walk into). How flexible you can be (at WL, your choices are Whispering Canyon, very popular and need a PS, Artists Point, expensive, nice and not someplace I'd take my kids to, or the snack bar. Or you can leave and try your luck at another resort or DTD or the park. If you are just as happy at the snack bar or Artists Point, or aren't starving and can go someplace else, you won't miss PSs. Starving moms sick of chicken fingers who don't want to take their kids to Artists Point get cranky - generalization based on personal experience).
This last trip we thought Le Cellier was fantastic - and will make a PS again for that. We enjoyed our meal at Teppanyaki - and that is on our "do again" list (although you can do the same meal at your local Benihana). Boma is a favorite here, but we won't go out of our way for that again unless someone we travel with really wants to go (it is worth it to check out the resort). We've always made time for Marrakesh - but that is one that you can usually walk into. A character meal (and I really don't think it matters to much which one, except who appears - the food is always mediocre) is a must do with a PS for every trip - particularly with small kids but we did it before the kids came as well.