First off, I always have rubber cement around and double stick tape. These two work on most items, and as long as you are not using the permanent kind of double stick tape, these two do not have to be permanent adhesives, which if you are mocking things up or just playing around with something that can come in handy.
An Exacto knife is a designer's best friend. They are excellent for cutting out just about anything. But I implore you to be very careful with them, they are extremely sharp and I have seen some intense Exacto injuries. So make sure those fingers are out of the way.
When you are using an Exacto you will need a cutting mat and most likely a ruler (for cutting straight lines). Both things are good to have on hand regardless. I actually have two cutting mats, one large and one small. I think I only got the small one when I was in school for traveling purposes, so it's not really necessary to have multiple.
I like to make boxes for mockups so I keep a bone folder on hand. It's not a totally necessary tool, but it sure does make things easier. I know I talked about them before, but they are basically for scoring edges so that you can fold materials easier.
I also like to cut out more complicated shapes (for some reason) but am no good at cutting circles with an Exacto (sidenote: I went to school with a girl who had a natural talent for cutting circles, so she was great to have around but you can only ask someone to do your cutting for you so much). So I keep a circle cutter on hand. The one I have is a little cheaper and a bit hard to use, but if you spring for a fancier one they work quite well and you no longer have to worry about cutting out perfect circles.
I also for some reason only make things with rounded corners. I dont know, I just like how they look better, so if I have the choice, I make my corners rounded. Therefore I also keep a rounded corner cutter (probably not the official name, but thats what it does) on hand.
There are other supplies I keep on hand such as a variety of pencils and pencils in various weights, acrylic paint, charcoal pencils, colored pencils, various paint brushes and erasers. I will probably post about that stuff later on, but it's a little more specific to me personally and my interests rather than general supplies.