Wrong, of course.
Not that these stats really mattered much back then. Your choice of weapons and armor were limited. Each town you found as the game went on sold conveniently better gear. There was little guessing involved. Was the shiny new weapon I found in the chest better than the one I already had? (Hint: The answer was always yes.)
In Warcraft, though, you have over 19,000 armor choices alone, and the stats associated with them get plugged into incredibly complex equations that differ from class to class, from spec to spec, straight on down to the talent level. There's spell power, sometimes presented as bonus damage or bonus healing -- that bit is easy enough to understand in a "more is good" way. But Blizzard introduces new players to spirit as a "mana regen" stat (never mind that there's also an MP5 stat) and intellect as a "max mana" stat (and marginally higher crit), not really clarifying the way it all affects your damage. They even throw in special PvP stats like spell penetration that don't do anything for the PvE player to muddy the water.
Making matters worse, all stats affect different classes and specs to different degrees. Blizzard is perpetually tinkering with the formulae, causing wild variations in effect from patch to patch. For newer players, the whole thing is a confusing mess. Developers seem to realize that things are getting a little too complex, and they're doing something about it in Cataclysm. For now, though, let's see what we can do to untangle the mess and explain how things work for shadow priests.
The pre-80 basics
In my early days, I had no idea what did what, so I figured I'd take a little bit of everything. "Oh neat, this Enchanted Pearl boosts all my stats! I'll take that one!"
If you're just beginning a shadow priest and are still in the leveling process, don't worry too much about stats. Equipment is just too disposable, readily replaced every few levels. When given the choice, however, give favor to gear that carries with it bonus spell power. Stamina is great for leveling, of course, because it boosts your max health. Focus on spirit and intellect for their basic abilities to increase your mana regen rate and max mana, since it'll reduce the time you need to spend sitting on the floor of the Barrens drinking milk.
Since priests can only wear cloth, you presumably won't be able to find a whole lot you can wear with other stats on it. To state the obvious though, you should generally avoid gear that has attack power, strength, or agility. Other classes get a heck of a boost from those stats, but as you can imagine, priests don't. Even armor numbers barely matter, since you'll be mainly relying on abilities like Inner Fire and Power Word: Shield to keep you safe from harm while soloing.
As a priest, you should never really be using physical attacks, even when you're out of mana. Default to using a wand instead. Leveling priests should make it a point to pick up a Lesser Magic Wand from the auction house or a leveling enchanter the moment they ding level 5. As you level, the stats attached to the wand will start to matter more than the damage from the wand itself, but you'll still need something for those rare situations where you're otherwise helpless to do anything.
After level 80: The simple version
If your post-80 goal is to mostly run heroics and raids as a shadow priest, then your number one concern will clearly be maximizing your damage output. The poster izolight over at shadowpriest.com (an amazing resource, by the way) was kind enough to put together a quick and dirty way of calculating what pieces of gear are better than others. It's not perfect, but it's a decent enough estimation for everyday use so you're not just guessing blindly:
Hit (up to the 263 ally/289 horde cap) = 1.88 Spell power
Spell power = 1.00
Haste = 0.98 Spell power
Critical Strike = 0.76 Spell Power
Spirit = 0.59 Spell power
Intellect = 0.22 Spell power
What does that all mean? It puts some math to what we already know -- Hordies should get their hit rating as close to 289 as possible (263 for Alliance if you'll be raiding with a Draenei) because it's such a valuable stat. The numbers also lend us the general notion that haste is better than crit, which is better than spirit, which is better than intellect.
On a more useful level, it allows us to convert all the stats on a piece of gear and boil down its effectiveness to a single number, pseduopower. As an example, consider the Frozen Bone Spike. It has 741 spell power on it, 59 points of crit, 67 intellect, and 59 spirit. (We really don't consider armor or stamina, since neither attribute to our DPS.) To make it comparable to other pieces of gear with different stats attached, we find the pseudopower through a bit of basic math:
741 + 59 (0.76) + 67 (0) + 67 (0.22) + 59 (0.59) = 835.39
The calculation shows that the Frozen Bone Spike acts like a weapon with 835.39 spell power with no other stats attached. Since everything's been converted to a single number, you can compare between weapons. The link above to shadowpriest.com has a lot of these "pseudopower" ratings already calculated for you, telling you what gems to use where for maximum DPS.
After level 80: The slightly-more-complex version
The actual way stats affect you is a challenge to explain. The pseudopower numbers above are a snapshot in time, reflecting how stats affect a player entirely outfitted with their best-in-slot gear (like the drool-worthy Phylactery of the Nameless Lich trinket) and only when a player is wearing that gear. The full best-in-slot set is presumably what raiding priests are supposed to aspire to, but a lot of it is obtained in wings of Icecrown Citadel that aren't even available to play yet. And even once they do go online, the odds of you ever having one specific build are, frankly, pretty poor.
Just going by the raw numbers above, you might get the idea that you should stack haste to the exclusion of critical strike rating. But no -- as you stack more and more of any given stat like haste, you actually increase and decrease the value you'll get from your next point of another stat. Statistics are synergistic. You have to hold a whole lot of variables constant to figure out how changing one stat is going to affect anything. And variables aren't so good at staying constant, on account of them being variables and all.
Think of it this way: If you had infinite haste but no spell power, you'd be rapidly firing off spells that barely make a dent in what you're attacking. If you have high critical strike but no haste, you'll be doing big numbers of damage, but those numbers would be coming along painfully slow. We have to strike some kind of balance.
So, what's an obsessive-compulsive shadow priest to do? The good news is that there are a couple of resources available for you to plug in your own gear and get some very personalized stat values so you can precisely plan your next move, gear wise. Of these, Simulationcraft tends to get the most respect. Some other shadow priests have gotten good use out of Rawr.
Or you can just swallow your pride and use the estimations above, accepting that you'll never really be able to tell the difference between the damage you get from wearing the 385.7 pseudopower Kilt of Untreated Wounds versus the 385.3 pseduopower Leggings of the Soothing Touch.
Perhaps someday in the future when the majesty (horror?) of Cataclysm is released upon the world of Azeroth, statistics will once again begin to make sense to the point that you won't need separate computer simulations to calculate what pair of pants to wear. Until then, though, at least we have a number of decent options to make some sense out of it all.
Hunger for more information about bending the light to your advantage? More interested in watching health bars go down than watching them bounce back up? Think it's neat to dissolve into a ball of pure shadow every few minutes? The darker, shadowy side of Spiritual Guidance has you covered.