The following are items I find myself using on a day-to-day basis while crafting away;
Glue Stick

Not that it needs to be this EXACT brand, but who can go wrong with Elmer's?! As with anything that I'm about to post, trial and error are the best means for finding a brand that works for you. The project I have used this the most for so far has been my Tissue Paper Bunting. (Stay tuned for a tutorial.) This project required nothing more than paper and a glue stick! Easy peasy, right?!
Double Sided Tape
9 times out of 10, I'll be using the permanent stuff. Unless of course you are affixing photos or something where you will be needing to peel off at a later time.
Fabric Scissors
It is extremely important to have at least 2 different types of scissors. One for fabric and fabric alone! This will insure they stay sharp so when you're trying to cut your ribbon, it's not fraying in all different directions. The second one for,
Paper Scissors
Or "All-purpose Scissors" as I like to call them. I'm awesome and use a Walmart brand that I picked up in the kid section. But no matter the brand, I use these puppies for EVERYTHING! I really need to break down and get an actual paper-cutter because my lines aren't the straightest in the world, but these will work for now! Lables, scrapbook paper, tape, you name it and I cut it. I've had my scissors for YEARS. However, I think it's time I need to upgrade to a pair of big girl scissors.
Paper Hole Punch
These come in such an array of shapes and sizes! If I were to own every single different kind, there would not be enough room in my house for anything else. The one I use quite frequently is the regular 'ol hole punch. I have two. 1/4" and one BIG 1.5" sucker. I'm always making labels and stickers with the larger one, while using the small one as something to lace ribbon through.
These are your very BASIC essentials, but trust me, they get me by. I will most definitely be adding more to the list as well as giving reviews for some of the non-freqently used tools I have.
What crafting tools can you NOT LIVE WITHOUT?