Seeing as Turkey is vying for a position in the EU and it's part of numerous European councils, Turkey isn't generally considered a Middle Eastern country.
I thought we brought democracy to Iraq (or I hope that's what we got out of that), and Egypt is holding their first election in forever in November. The area's getting better overall in terms of democracy it would seem, with or without our protection of them.
According to that Israel is a 'Flawed democracy' and Lebanon is a 'Hybrid regime'. I cannot say I'm familiar with the political system in Lebanon, but I do know they've been having some major issues with their government lately. IIRC they haven't had a functioning executive branch since they agreed to comply with the UN investigation into the assassination of former Prime Minister Rafiq Hariri. Hezbollah (effectively the military of Lebanon and a very strong political power) is extremely unhappy with this because the allegation is that they assassinated him.