Both the words icon and idol are used in the New Testament.
The Greek word eikōn (icon) is translated portrait in Ma 22:20, Mk 12:16; and Lk 20:24.
The Greek words eidōlothytos and eidōlon are translated idolatry and idol in 1 Co 10:14,19 and passim.
From both the Catholic and Protestant traditions, Christians (with very few exceptions) do not oppose the use of icons, since Jesus Himself handled coins with icons on them and taught His followers to "render unto Caesar [whose portrait was stamped onto coins] the things that are Caesar's." Since an icon is simply a likeness, a portrait, or other representation of a human being (e.g., a statue), there is no biblical reason for not producing them in whatever medium (e.g., oil paints, watercolors, pencils, mixed media, granite, wood, cloth, paper). Jesus was, after all, "God's self-portrait in human flesh" (Gerald L. Sittser, Water From a Deep Well, p.177).
Where Protestants often part ways with Catholics over icons is when Catholics actually bow down to an icon and in a sense pray to that icon, using it as an intermediary between them and God. A case could be made that this form of interaction with an icon is unbiblical, since as someone has already pointed out, above: there is only "one mediator between God and man [and that is] Christ Jesus" (1 Ti 2:5).
This "drawing of the line" by Protestants is, on the one hand, understandable and has a biblical basis. On the other hand, if an icon (religious or otherwise) is simply looked upon, appreciated for its aesthetic and spiritual appeal, or if it becomes in effect a "springboard" for contemplation and inspiration as the "message" of the icon in a sense communicates spiritually with the beholder, then there is no logical reason for Protestants not to have icons, including statuary, in their churches. It's just a matter of tradition for them not to!
Idols are a different matter. In the 21st century we may not fashion idols of wood, metal, and stone, but many people in the modern era still make idols of something tangible, whether it be money, possessions, food, land, houses, or other people. That is why the apostle John warned his children in the faith:
"Dear children, keep yourselves from idols." (1 Jn 5:21)
Albert Martin defined a god (or idol) as follows, and I paraphrase:
The one from which you seek your highest satisfaction, to which you yield supreme allegiance, for which you will pay your greatest price, upon which you pin all your hopes.
In conclusion, the subject of icons and idols is controversial. Many if not most Roman Catholics realize icons exist to enhance and inspire their worship of God. Some Catholics and even Protestants, however, treat icons (and relics) as good-luck charms with magical powers, which is clearly not biblical. Moreover, praying to an icon is worse, because it borders on idolatry. As Paul cautioned the Corinthian believers,
"Therefore, my dear friends, flee from idolatry." (1 Co 10:14)
God does not endow any thing with a part of Himself. To suggest such a thought in word or deed borders on animism, and we must never worship the creation rather than the Creator. Although God is immanent and omnipresent, more importantly He is transcendent (Isaiah 55:8,9).