If you're curious what language is spoken in Egypt, then you might be surprised to hear that answering "Arabic" is somewhat of an oversimplification. In fact, like other Arabic-speaking countries, the official language of Egypt is not technically a native language to its inhabitants at all (see below). Egypt is far from monolingual or monocultural and in fact, has a rich linguistic history stretching back thousands of years before the arrival of Arabic culture.
The most widely spoken and common language in Egypt is, broadly speaking, Egyptian Arabic. Although it's the spoken by practically all inhabitants of Egypt, it is still not recognized as an "official language" by the Egyptian government.
Egyptian Arabic is a broad term that covers many sub and regional vernaculars depending on geographical location. For example, Nubians in the far south of Egypt speak a very different variety of Egyptian Arabic to Cairene Egyptians (Cairo) or those in Alexandria or Sinai. Each sub-dialect is a product of centuries of local and foreign influences.
Prior to Arabic arriving in Egypt in the 7th Century due to the spread of Islam, Egyptians spoke Coptic (now mostly extinct apart from Coptic Orthodox religious liturgy). Coptic, along with Berber, French, English and others, have influenced Egyptian Arabic heavily.
Contrary to what many people are led to believe, Modern Standard Arabic isn't actually spoken by anyone anywhere as a native language.
That being said, MSA, is listed as the official language of Egypt and is used in all official and formal settings. This includes politics, news and media, books and educational material, and religion (although the Classical form is more prevalent in religious contexts). When visiting Egypt, you will encounter Modern Standard Arabic everywhere.
Classical Arabic is the Arabic of the Quran, and Modern Standard Arabic derives itself primarily from it (along with other modern influences).
We've already mentioned Coptic above.
This is the what many regard as Egypt's indigenous language - the linguistic descendent of the language of the Pharaohs. It is now primarily a liturgical language of the Coptic Church.
Other predominant languages in Egypt are English, French, Nubian, Bedawi (Bedouin) and Siwi (Siwa).
In recent years, other Arabic speakers have increased enormously increasingly the presence of other dialects in Cairo and Alexandria.