Spell Haste is an interesting stat in theory. It reduces the cast time of your spells, and is supposed to be a double-edged sword, increasing the Damage-Per-Second of your spells, but also increasing the Cost-Per-Second. However, for a variety of reasons, I think having Spell Haste on gear has actually weakened the game in several respects.
1. Speeds up the Game
The most obvious thing spell haste has done is speed up the game. Everyone casts faster, does damage faster, and heals faster. Which leads to people taking damage faster as well. I think that WoW has gotten a little bit too fast, and could stand to be chilled out some.
2. Emphasis on Spamming Casts
You really only see the power of Spell Haste when you are spamming spells. To take advantage of a small reduction in cast time, you need to be hitting buttons immediately, in quick succession.
3. Blurs the line between Short Casts and Long Casts
With lots of spell haste, there's not much difference between spells with short cast time and spells with long cast time. This has causes short cast spells to be undervalued, and instants to be greatly more powerful.
For example, if spell haste did not exist, it's possible that interrupts could go back on the GCD, making it harder to interrupt short spells, and making Curse of Tongues more valuable, even in PvE.
4. Prone to "Magic Numbers"
If an ability rotation includes a spell with a cooldown, spell haste means that certain "magic numbers" will exist. These are values of spell haste that allow you to squeeze an extra cast off while the first spell is on cooldown.
For example, baseline you can go Holy Shock, 3x Flash of Light as a baseline. But there is a value of spell haste where you can squeeze in an extra FoL while HS is still on cooldown. And an even higher value where you can squeeze in a fifth FoL.
I don't think this level of complexity--actively changing a rotation like this--is good behavior for a stat to exhibit. It makes people overly reliant on theorycrafting and spreadsheets.
5. Messes with the Global Cooldown
The Global Cooldown is the "heartbeat" of WoW. I think that allowing spell haste to alter the GCD was a mistake. It plays havoc with the rhythm of the game, and has led to random spells having odd GCDs. In my view, the game just plays much better when there is a standard 1.5s GCD on all abilities.
I also think that too many abilities are now off the GCD, and that has also contributed to the excessive speed.
That's not to say that reducing spell cast times is entirely bad. I think that it is a quite appropriate effect for talents like Improved Fireball. Talents can also allow for a significant change in a specific spell's cast time, rather than a very small reduction in the overall cast time. Reducing cast time on specific spells is a good effect for talents or possibly glyphs, just not a good effect for a gear stat.
However, the general idea of the stat, increasing DPS while also increasing cost-per-second, is a good notion. With the integration of spellpower into Intellect in Cataclysm, perhaps spell haste could be retired as well. Replace it with "spell infusion" a stat which directly increases SP and Cost, without changing cast time. This would give two knobs to balance the stat, rather than indirectly balancing both through cast time.