In practically all dialects of (British) English, the word "idea" would generally be followed by an 'r' sound when followed by another word beginning with a vowel. So for example in saying "it was his idea and decision", this would usually be pronounced "idea-r-and decision". The phenomenon occurs in many places where you have a word ending in a vowel followed by another word beginning with a vowel and they are 'closely linked' syntactically, e.g. "law-r-and order", "Canada-r-and America", "he took the law-r-into his own hands" etc.

This occurs essentially because it's a natural phenomenon of language to have some strategy for 'linking' words together. French has a similar phenomenon involving 'latent' consonants (principally [z]), Spanish allows vowels to 'merge' into the same syllable, etc.

Update: there seems to be some disagreement about the exact extent of this phenomenon. In his article in the Blackwell Handbook of English Linguistics, Michael MacMahon (2008) describes it as:

"now very common in many accents of non-rhotic British English"

though without giving any actual data. Gick (1999), one of the articles referenced by the Wikipedia entry, comments:

"[...] the available data, which has centred almost exclusively on only two dialects: Southern British Received Pronunciation [...] and the dialect of eastern Massachusetts [..]. No other r-intruding dialects have been described which provide evidence bearing conclusively on the controversy."

However, I think by "the controversy" here, the author means "how the phenomenon is to be analysed phonologically" rather than whereabouts the phenomenon actually occurs. What seems to have happened is a few studies have focussed on certain specific dialects, but we shouldn't conclude from that that the phenomenon occurs only in those dialects.