What's the word for words that roll off the tongue?

Mellifluous, maybe?

I'm not sure if you are looking for an adjective that describes them, or a noun.

Mellifluous seems like a good fit. It itself is pleasing to say (a bonus!). :-) It comes from the Latin for "flowing" and "honey".

"Phonaesthetics" describes the study of such things and the appropriate word would be "euphony" or "euphonious":

A pronunciation of letters and syllables which is pleasing to the ear. (wiktionary)

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Edit in response:

The phrase "articulatory phonetics" describes "how humans produce speech sounds via the interaction of different physiological structures." Phonaesthetics describes the more abstract aesthetics associated with speech. "Phonetics" includes the physical motion of speaking. Therefore, I claim that phonaesthetics includes the physical aesthetics of speech. "Euphony" refers to the pure sound aesthetics but either of these two terms should work:

• phonaesthetics
• articulatory phonaesthetics

The others are good Romance derivatives. A recently popular phrase with obvious meaning is:

good mouth feel

It seems that no word we know of is quite right, so perhaps a word should be crafted from the parts we have lying around in this thread! Specifically, I think "mellifluous" and "euphony" offer promise, even though (as the OP points out) they both are associated with an act of pleasant hearing rather than the pleasant somatic feedback from the mechanical act of speaking.

This, it seems to me, is easily fixed by drawing on another beautiful word derived from Latin, "loquacious." Though this is most commonly taken to mean "talkative," the root in Latin (loqui) simply means "to speak."

Thus, I submit for consideration either of the two following constructions:

Melloquious - Mel+loqui - (like) honey to say

Euloquious - Eu+loqui - good to say

If a loan word from another language can be found, that might be a better alternative, but if there is no fitting and compelling word to be found, then perhaps it is up to us!

I was also looking for this word and never found a good one. I like the suggestions given here but wanted to add the word that I came up with for this purpose. Eulalaiic (eu-lah-lay-ic) Etymology- eu = good and ululation= high pitched trilling sound involving movement of the uvula associated with high emotion. Plus eulalaiic is really eulalaiic

Fantysheeny might provide a close-definition and also a fun word that is an example of the phenomenon in question. It is a dialect word from Devon in the far southwest of England.

Fantysheeny: A FANTY-SHEENY is anything showy or impressive. It derives from ‘fantoccini’, an Italian word for a puppet show. [Haggard Hawks]

I'm looking for a single word for words that are fun/easy/pleasant to say—words that roll off the tongue, so to speak.

Mellifluous is really a good word to use here. If not mellifluous, then I suggest dulciloquious.

From the OED:

Dulciloquy: A sweet or pleasing manner of speaking; sweetness of speech.

Origin: A borrowing from Latin. Etymon: Latin dulciloquium.

Etymology: < post-classical Latin dulciloquium sweet speech (from 12th cent. in British and continental sources) < classical Latin dulcis sweet (see dulce adj.) + -loquium < loquī to speak (see -loquent comb. form)...

1998 S. Byrne H, v., & O 135 Harrison's poetry..does not commend the tongues of fire of dulciloquy and poetic eloquence as capable of bringing redemption

So a person having a sweet voice would be dulciloquent.

Dulciloquent is defined by the OED as:

Of a person: sweet-spoken. Hence also of an utterance, style, etc.: characterized by pleasing or mellifluous language.

You could use dulciloquent but I guess dulciloquious is better than dulciloquent (in this context).

Dulci means honey/sweet/pleasant, loqui means speak, -ous is a suffix which means of the nature of. So dulciloquious actually means pleasant/sweet to say.