If Iran wins, you could see Saddam getting overthrown by a Tehran-backed Shi'a revolt in Iraq. Also, Shi'a militancy in the Gulf Region would flare up again, as it did during and immediatly after the Iranian Revolution. You may see successful Shi'a Islamist revolutions in Qatar, Oman, Kuwait, etc., or, if they fail, drawn-out guerilla wars.
Turkey, Egypt, Syria, and especially Saudi are going to be really nervous about a strong Shi'a power that is openly hostile to them.
If Shi'a uprisings succeed (probable, about 50-50 in the Gulf) you will see Iran treating them as client states. Things will soon turn sour, though, as Arab-Persian antagonism, xenophobia, and distrust will probably tear apart any ideas of "Islamic Unity."
Most likely this break will occur in the aftermath of Khomeini's death, with Shi'a Arab leaders regarding Khamenei as a "revisionist" (think a Shi'a Islamist version of the Sino-Soviet split)
The result? Perhaps a resurgance of Arab nationalism against Islamism (which could be cast as a form of Persian imperialism); big energy concerns for both East and West over de-facto Iranian control over the Persian Gulf; Islamist states in the 1990's that may look to the West for support against an Iran that seeks to reassert dominance.