The Middle East would still have great power tensions without the rise of political Islam. I suspect that Iran and Saudi Arabia would still be feuding over hegemony in the Middle East, while a more secular Turkey would still be another player in the Levant and Iraq.
Public health would still be a major issue if SARS, Ebola, and the Swine Flu happen as OTL.
Without Islamist terrorism, the FARC in Columbia would be the single deadliest terrorist group. The humanitarian crisis and instability associated with the First and Second Congo Wars and the Rwandan genocide would still occupy international headlines and the agenda of international organizations.
There might even still be a conflict in Chechnya if it remains a secular nationalist cause. Ossetia, Abkhazia, and Nagorno-Karabakh would still be conflict zones in the Caucasus.