It's annoying that there's no easy way to create new reminders in Mountain Lion without launching the Reminders app itself. But an anonymous Hints reader did figure out a way to do so with Automator. The only hitches: All reminders you create with this workflow must go to the same list, with the same priority, and you can't automatically assign a due date.
Open Automator and opt to create a new service. At the top of the Automator scripting pane, choose No Input from the Service Receives drop-down and Any Application as the In option. Next, open the the Text actions library, choose Ask for Text and drag it to the right-hand part of the Automator window. Enter a prompt, such as
Enter a Reminder. From the Mail library, choose New Reminders Item and drag that below Ask for Text. Choose a list to which you want to add the item. You can select a priority, but you probably don't want to select a Due Date. That done, save the service.
Now open the Keyboard preference pane in System Preferences, open the Keyboard Shortcuts tab, and find the Services section on the left. Select the service you just created and assign a shortcut to it. Now, you can hit that keyboard combo from any Mac app, and you should get a dialog box prompting you to enter a reminder.