A simple and immediate swap of an everyday item that is painless and a complete no-brainer is Cellulose Tape instead of the usual Plastic Tape.
Cellulose is biodegradable and if the word "Cellulose" rings a bell, it's probably because back when you learned about plants and photosynthesis in school, Cellulose was mentioned. It's the substance that makes up plant cell walls and since all plants make it (and some oceanic lifeforms as well), it is in great abundance on this planet. In addition, this tape can be torn by hand so you don't have to worry about that annoying plastic tape dispenser. It goes without saying but Plastic Tape is not recyclable, and I can't think of any way to reuse or repurpose used Plastic Tape at all (if you can, please let me know!)
I've found this tape on Life Without Plastic's website: http://lifewithoutplastic.com (they are an amazing resource for many practical items) but if you do a quick search you will find many other options for Cellulose Tape online. The thinner tape I use for wrapping presents while the thicker tape is great for shipping boxes.
I often sell my gently worn clothes online and I've used this tape to ship those boxes all over the country! Honestly, if I had to choose, the thicker tape is really all you need as you can also wrap presents with it so next round I will just replenish the thicker tape instead of both like I did last time. Less is more, right?
When you find yourself running out of tape, instead of purchasing the usual Plastic Tape, please consider purchasing Cellulose Tape or better yet, order some now so when you run out, you won't be forced to buy Plastic Tape because it's more conveniently available.
On an exciting side note, since using this tape I've become intrigued and smitten by Cellulose. I really see it as a great plastic alternative and replacement. My hope for the future is that all of our food that comes in plastic now will soon come in wrapped Cellulose instead.