Is there a reason to not disenchant extra cards?

When a card is changed or nerfed the disenchant reward changes to the same as the enchantment cost for a few weeks. Unless you really need the dust for crafting specific cards it's a better long term investment to wait. Best scenario you get 4X the dust if you wait.

But, if you do need specific cards for your decks it's probably not worth it to speculate on future nerfs. Card changes are not common, so this strategy is most useful if you plan on collecting every card, or every golden card.

Patch notes in the client will list such changes. It is also common for changes to be discussed by streamers or in youtube videos.

The Card Changes page on Gamepedia lists previous changes and ones about to be changed. You can subscribe to notifications for the above page to, most likely, ensure you do not miss a card change. To do so add "Card_Changes" to your watchlist after making an account, validating your email and enabling watchlist notifications in your settings. [more info]

NOTE: This answer is historic now as the game has changed. See Annan's Answer.

Disenchant them! There is no reason to keep any extra cards. Once you have 2 of a card, you can use those two in as many decks as you want.

Additionally, there are two excellent answers to this question about the science of disenchanting cards in Hearthstone that you should also read.