La Real Academia Española doesn’t set the pronunciations of Spanish words in the terms of an international phonetic standard like IPA or SAMPA.
Theeð, actually.
Everyone has covered everything on the subject I would have said. Just adding a sidenote that Arabic has both sounds: د dāl (voiced dental stop) and ذ dhāl (voiced dental fricative). Although, as Nava observed, the Arabic etymon for Cid is سيدي sīdī ‘my seigneur’ or just ‘sir’* with dāl, not dhāl.
*from Classical Arabic سيّدي sayyidī ‘my drighten’. The feminine equivalent is سيّدتي sayyidatī ‘my lady’, because -t- makes the feminine gender in Afro-Asiatic languages.
Same difference as between Greek δ (dhelta) and ντ (ni-taf, pronounced /d/).
Icelandic has /ð/ (written <ð>), but it doesn’t have /d/. Hebrew and Finnish used to have both /ð/ and /d/, but now they have only /d/.
Although Spanish uses the same letter to write both sounds, it’s no problem, because they are differentiated positionally. English on the other hand, writes both phonemes /ð/ and /θ/ with the same “th” :smack:.
Most of the Saami languages have both /ð/ and /d/, written <đ> and <d> respectively. So you can tell them apart!
And what I’m saying is, first, using Wiki as the source has the problem of things like that happening. The same source has also suffered from things such as someone going to the entry for every king he could think of and adding “possibly gay”, from people being granted titles that never existed, or of names being mistreated six ways to Thursday.
And it also matches with what I said: the phoneme is always the same.
This.
ETA: No, I’m not dissing anyone! 
The phoneme may always be the same, but there are at least three different allophones. So no, it’s not pronounced always the same any more than a P or a T in English is always pronounced the same.