Zan is 100% right. All we have are approximations, and most emulators have wildly incorrect palettes if you're looking for the authentic NES look.
If you want a (non-authentic) look closer to the colors as the NES's internal data represents, then the official Megaman 9/10 palette is a safe bet. It's not 100% but its adjusted for modern displays. This is NOT the colors the NES put out to a TV though.
If you want to actually go authentic, then you need the NTSC approximation palette. This makes it look exactly how you remember it from the old days. This is the color palette your NES pushes out to an NTSC TV, and it's different than the color data found in the NES itself suggests.
The palette images I constructed (attached for you below) have ordered palette indexes that are exactly the same. You can swap one palette with the other, and everything lines up. This way you can view your palette'd images in either palette to see how they look. One of them is the Megaman 9/10 palette, and the other is the authentic NTSC palette. The NTSC palette was constructed from examining the actual output signal of an NES. It's as accurate as you're going to get.
Also included is a sample of the difference between the two, using a screen shot from Megaman 5.
If you want it too look like a real NES, then the NTSC is the palette you're looking for.