Well, a neutral Nature is actually always a no-go.
Neutral may not seem bad at first sight, and it isn't necessarily bad. But you are not benefiting from anything. The thing about neutral nature is... you're not sacrificing anything, but sometimes it's better to sacrifice something to gain something. For example, many Pokemon are just one-dimensional, and would either like a boost in Attack or Speed. They usually have a stat they do not use (for example: Gyarados' Special Attack) and wouldn't mind if that was cut to raise their primary stat. A lot of Pokemon in the metagame tend to boost their Speed to outrun things, and that 10% boost makes a huge difference at times (base 100s, for example, can have a max of 299 when neutral and 328 when at positive). For stats like Speed, which is very absolute and only takes only one point to outpace the other guy, it is ideal to have it boosted.
As for mixed attackers? Normally they want one of their defenses lowered. Stuff like Infernape, who has relatively low Defense, do not mind losing of it without compromising either Attack or Special Attack but boost Speed. That speed is insanely crucial to outpace many things. If you're going for a mixed attack Swampert, you do not want any of its defenses compromised nor its attacks. However, it is quite slow, so it does not mind the speed drop as much as the others. That's just an example, but it all comes down to what you want. Want to make it a physical attacker? Then you know you can drop the Special Attack stat when it comes to picking a Nature. You have to know which stat to drop when going mixed, but you do really want a stat to be boosted.
Very few Pokemon in the competitive metagame want to stay neutral. Jump out of the fence and get a boost someplace.
PS: Questions about in-game mechanics like this are perfectly suited for the
Have a question? Ask it here! thread in the Orange Islands section or the
Simple Questions/Requests thread in the Wi-Fi section.