dream:  Old English had a word drēam, which meant ‘joy, merrymaking, music’, but it is not at all clear that this is the same word as modern English dream (the recorded Old English words for ‘dream’ were swefn and mǣting). Semantically, the two are quite a long way apart, and on balance it seems more likely that Old English had a homonym *drēam ‘dream’, which has not survived in the written records, and which was perhaps subsequently reinforced by Old Norse draumr.
Both these and the related German traum and Dutch droom have been traced back to an Indo-European base denoting ‘deception’, represented also in Sanskrit druh- ‘seek to harm’ and Avestan (a dialect of Old Iranian) druz- ‘lie, deceive’.
mid-13c. in the sense "sequence of sensations passing through a sleeping person's mind" (also as a verb), probably related to Old Norse draumr, Danish drøm, Swedish dröm, Old Saxon drom "merriment, noise," Old Frisian dram "dream," Dutch droom, Old High German troum, German traum "dream," perhaps from Proto-Germanic *draugmas "deception, illusion, phantasm" (cognates: Old Saxon bidriogan, Old High German triogan, German trügen "to deceive, delude," Old Norse draugr "ghost, apparition"). Possible cognates outside Germanic are Sanskrit druh- "seek to harm, injure," Avestan druz- "lie, deceive."
But Old English dream meant only "joy, mirth, noisy merriment," also "music." And much study has failed to prove that Old English dream is the root of the modern word for "sleeping vision," despite being identical in spelling. Either the meaning of the word changed dramatically or "vision" was an unrecorded secondary Old English meaning of dream, or there are two separate words here. OED offers this theory: "It seems as if the presence of dream 'joy, mirth, music,' had caused dream 'dream' to be avoided, at least in literature, and swefn, lit. 'sleep,' to be substituted ...."
Words for "sleeping vision" in Old English were mæting and swefn. Old English swefn originally meant "sleep," as did a great many Indo-European "dream" nouns, such as Lithuanian sapnas, Old Church Slavonic sunu, and the Romanic words (French songe, Spanish sueño, Italian sogno all from Latin somnium (from PIE *swep-no-; cognate with Greek hypnos; see somnolence; Old English swefn is from the same root). Dream in the sense of "ideal or aspiration" is from 1931, from earlier sense of "something of dream-like beauty or charm" (1888).