This is somewhat a complicated concept... on the most basic level 'vibrant' usually contrasting colors. During the creation of a piece of pixelart, it's palette will make continual changes as new tones are added in. You try to balance whatever it is that you are making *as* you make it. Its very hard to create all the exact tones you need before you begin a piece.
[BAISC PIXEL COLOR THEORY]
-pixels are much more exact than natural media so you must 'learn' what colors are light and dark
*the follow values are the HUE of a color (using RGB to select colors is alot more complicated... I only know like two artists who do it)
*I do not include most of the inbetween colors (teal violet, magenta etc...its not necessary right now, I'm only included commonly used colors)
[MIDTONES] (the 'base' tone if you will)
+red:5-25hue or 340-355hue
+orange/brown:25-40hue (the less saturation this hue has, the more brown it becomes)
+yellow: 40-50hue
+green: 65-80hue (darkers greens 'hue:120ish' generally look VERY bad unless they are confined to a small area on a pic)
+blue: 200-215hue
+purple: 220-245hue
[SHADOWS] (where light does not hit...)
+red: 0-10hue or 330-340hue
+orange/brown: 10-25hue
+yellow: 20-30hue (note the shadows of yellow tend to be orange or brown)
+green: 80-95 or 120~145 (again...there usually isn't alot of dark green in an image, even a forest scene, so this hue:120+ is ok)
+blue: 220-245hue (note...the shadows of blue tend to be purple... perhaps its a pattern...)
+purple: 225-245hue (purple generally is its own shadow)
[HIGHLIGHTS] (where light directly strikes an object...used to make specfic objects POP)
-This section is complicated. It involves hue shifting to figure out
-highlights are generally done by shifting your midtone hue to the next brightest color
****show hue-slider****
-red/orange/brown: maximum hue: 35-50 (aka yellow~yellowish-orange)
-yellow: maximum hue: 55-60 (any higher and you get green)
-green: maximum hue: 55-65 (yellow is brighter...thus it highlights green)
-blue: maximum hue: 160-195 (notice the huge-ass range... blue is just weird that way...most greens/teals/light blues can highlight it beautifully)
-purple: maximum hue 200-210 (aka blue) OR 300~345 (again huge range, magenta/violet can highlight purples as well)
[COLOR COMPARISON]
-yellow->green->orange/brown->red->blue->purple
-some colors are brighter than others...its just how colors are
-yellows are generally the brightest 'colors' aside from white(s)...
-colors blend best if 1)they follow the hue rainbow-thing 2)the tones are seperated by an area of shadow
Here's an example of how I go about creating a simple grass dirt and rock landscape.
[STEP 1]

-choose basic tones to work by choosing one midtone and one shadow tone for each color you want
(since I am doing grass I need two tones of green, rock: thus two tones of grey, dirt: two tones of brown)
-decide on the style/mood of the piece
(I am doing two varients, brighter and cheery, then another that is highly contrasted)
-when creating a scene you must decide what color the light is
(I use yelowish highlights and purplish shadows)
(also the highlights and shadows do NOT have to match...it creates that vibrant look you see in alot of demo-scene art)
-now lay down the basic shapes...
[STEP 2]

-again add one more tone per object (new tone somewhere between your two initally tones), detail the scene further...
-I am leaving some areas 'un-finished' becase if its generally faster to choose 6 tones per color initially (but that can be overwhelming for this explaination)
[STEP 3]

-continue adding tones till you have detailed the scene the way you want it
-focus on a few areas till you know how many tones you will need to detail everything properly
-as you add new tones you will need to re-contrast your old tones, this is where the initial color theory, at the top, comes in...
-you will have to eye-ball your scene to decide how much contrast you want, for this first mockup, I want very little, so I keep the saturation and luminance between each color fairly low (about a 5-6 point different in luminance for each tone)
-remember, you DON'T arbitraily shift each new tone down by 5 lum/hue, the difference is based on how much you want a spefic object to stand out
*ex: dirt...dirt is not highly contrasted...its flat and dirty so I keep a low lum-decrease but a keep a steady hue-shift
-remember how your lighting the scene, in this case things closer to the ground are darker and less detailed/contrasted than the things higher up, its tricky and you only learn how to do this properly by heavy study of pixel art
*here I noticed my grass was getting overly bright...blinding really, so I 'muted' it by darkening it and lowering its contrast
[STEP 4]

-this part is fun, you now must unify your pallete, even if your grass is 'green' your dirt 'brown' and your rocks 'grey' your light-source will blend them together (and the fact the scene is so #($*#'ing small)
*ex: take a high-res cg and zoom out... you'll see how everything begins to merge, blend, and distort
-pixel art thrives on controlling the color of each individual pixel, it allows you to create very clear and concise images at any resolution
*unlike a CG, where the image is generally very large capturing the entire scene, pixel art is relatively small, focusing on various elements within the piece (sprites for example)
*there are of course numerous exceptions...however it remains true that high-quality pixel art tends to have 'prettier' colors than a cg, because the pixelartist has more control over how the colors are manipulated
-various ways to 'unify' a palette are by a)lowering contrast b)making all objects' hue's closer together c)adding shadows between objects
*shadow example: grass meets dirt, shadow on the edges, rock meets 'whatever': crevices added as an excuse to add a shadow tone
-one other way to blend tones is to blurr the hell out of the surrounding area
*blurr example: crevices near rock, tiny indistinguishable details prevent your eye on focusing on that area creating a 'blurr/blend' effect
*blur example #2: grass meets dirt: adding small patches of grass scattered in the dirt helps guide the eye into the brown easier
*because the dirt is generally lighter, you slowly 'loose' the darkest green tone, this causes the new grass to be less contrasted and thus blend easier
+green: needs to be darker still (too overpowering, green tones take awhile to unify, one of the trickier colors)
*needs to be shifted closer to yellow as well
+brown: needs to be more 'yellowish' to blend better with the grass
*since yellow is a lighter color, more contrast is needed as well
*since the contrast was added, I had to replace several tones I laid down near the rocks, since they were too dark (I used the next lightest tone)
+grey: minor contrast tweaks, saturated the darker tones to blend better with the ground
*remember when choosing tones, their colors are BASED on whatever tones are nearby (if you plan on having a decent looking image at least)
[STEP 5]

-this last step is full of subtle tweaks, and finishing off the image
-added two more dirt tones, one highlight and another detail tone
-{more to come}
[ALTERNATE EDIT]
{FINISHED!}

-wilder colors make an image more vibrant and dynamic
-contrast makes an image look more real...and dynamic
-shadows make an image look even more real and more dyamic
-you cannot just shift the hues around, darker hues (purple/red etc) need less contrast than brighter colors (yellow green etc) to look good, too much contrast will fudge up the viewer hehe
-initially you do just play with the hues...but then you must unify again (modify contrast, saturation etc)
-note that you can actually shade by using hues, darker tones use darker hues (usually) this requires less of a saturation/luminance change between colors
*removed one tone from the bottom layer to make the viewer focus on the 'cliff'
*add a light-fall-out, the further away from the viewer, the darker the scene gets (purples near the top of the scene)
I hope what I put so far is of some help, if you have any specfic questions on anything I wrote, just ask.