Why do you sometimes write down one word while actually intending to write another? I've caught myself writing (typing) "possible" instead of "possibly" a few times over the past few days, while I do intend to write "possibly". Only upon rereading the sentence I notice my mistake.

It is not a typo. I am able to touch-type on a qwerty layout on which 'e' and 'y' are both written using a different hand, and different fingers. The keys are two keys apart from each other.

A simple google search for "psychology writing wrong words" didn't show up any immediate relevant results. I did read about a Freudian Slip, but it seems highly unlikely I would make such a mistake due to an "unconscious ('dynamically repressed'), subdued, wish, conflict, or train of thought".

Is there any psychological phenomenon explaining why I would make such an error?
The speech error taxonomy on Wikipedia that Jeromy Anglim links to in his answer is pretty comprehensive. If you're interested in learning more, I would suggest reading some articles by Gary Dell (e.g., Dell, 1986). He is, in my opinion, the expert in this domain. He has used neural networks to explain speech errors of different types.

When mentally planning the next word in a sentence, we must choose the appropriate lemma. By selecting the units in a neural network that correspond to a certain lemma, it spreads activation to the corresponding morphemes, which in turn spreads activation to its corresponding phonemes. When the activation of a phoneme unit exceeds a certain threshold, it is selected for utterance (e.g., spreads activation to the motor units that allow us to speak).

However, this model is susceptible to retroactive and proactive interference: if we have just spoken another word that requires a different morpheme, its activation may exceed that of the target morpheme because of (for instance) undue attention or neural noise.

The same model can predict typographic errors as well: phonemes spread activation to orthographic units, which spread activation to the proper motor units which control our fingers.

Interestingly, speech errors rarely violate the rules of syntax, morphology, or phonology (even though they may make little sense semantically). Psycholinguists can use this fact in order to infer the structure of linguistic rules without having direct, conscious access to them.

Dell (1986). A Spreading-Activation Theory of Retrieval in Sentence Production. Psych Review, 93, 283-321. Retrieved from
http://129.237.66.221/P800/dell1986.pdf