Here's my personal thoughts on this if it matters:

Melee is a great game from what I've seen, and it's been at the top and praised by many for a good amount of reasons. The top tier hype is intense, the fanbase is huge, and overall it's a very, very intense and exciting game. I'm sure there's more to it, but you get my drift, I hope.

Brawl came along, and basically felt like the opposite of Melee to many. It felt slow overall, and was just generally designed to be uncompetitive in general, especially when you're comparing it to Melee. Sakurai's intentions at the time were to cater to the more casual (for the severe lack of what I feel could be a better word) audience. Yet it was new and fresh at the time, and it also divided the community (from my research), and apparently caused quite a lot of drama.

With Smash 4 on the horizon, I could see people fearing another split, and that would be reasonably something to be nervous of.

But it doesn't have to happen.

I'm not saying that Melee players should just let it go and switch to the new thing, nor to just exclude Smash 4. You can choose to join in or not to join in, just don't automatically berate the new game while it's still fresh. If anything, the berating in general needs to end. A person plays a game you don't like, big whoop.

Each of the Smash games, including Melee and Smash 4, have something unique about them that attracts certain players, and that's honestly a great thing. While we should push for Smash 4 tourneys, we should also try our best to include the Melee as well so that no-one is excluded. We can co-exist easily.

This also includes all of the previous Smash games (also counting Project M.)

tl;dr: I'll quote something from @TheMoon112 that I think many will agree on: Smash 4 isn't going to kill Melee. It's gonna be an addition to the roster. Otherwise, you really should read the whole thing.