If it's the lucrative thing to do, and is not a hassle, sure. I no longer play WoW, but here's an example: While I was leveling my rogue from level 43 to 45, I exclusively grinded some dragons in Dustwallow Marsh. The reason I did this was because the dragons were relatively simple mobs, they skinned leather which sold for good money in the AH, and it was good exp. The result was that I amassed around 550g after my work was done, and even had my first world epic drop in the process.
What did I do with that money? Well, I willfully stopped playing once she reached level 45, but I had the notion that I would return to the game when circumstances allowed for more leisurely play time. So I got my old, deleted level 60 priest restored, now bare naked and shit poor, and sent the poor sod some money so that he would get an epic mount. I also played for a couple of levels in Outland so as to get the guy equipped with some standard issue greens. My motivation was that I could always make more money with my rogue. This was before the exp nerfs and dungeon boosts SolitaryPenguin is referring to.
For me a grind becomes much more meaningful when -
i. My character's efficency is not bound to a limited resource. So I could tolerate, even enjoy grinding with my combat rogue efficiently dicing through enemies with not much effort and a paltry commitment of a bandage every fifteen to twenty mobs. My shadow priest is as fun to play as my rogue, but leveling and level-grinding was more of a pain with him simply because he had to drink every five mobs or so.
ii. There's a high density of mobs. This is critical. It minimizes additional downtime and maximizes the experience you're getting.
iii. There are financial benefits to doing it, as outlined in the first paragraph.
Note that in the case of the priest i. often plays against this point, as a priest has no way of self-regenerating mana between battles, unlike mages (conjure water), warlocks (life tap + life drain). Paladins don't spend mana all that much, either, and nor do feral druids -- but I don't think feral druids are very fun! And It's important to pick your mobs well. Humanoids are almost always preferable to non humanoids, except when skinning/farming a certain item is involved.