One of my first rules of thumb when it comes to wrapping is to make it beautiful. I take joy in wrapping packages, as friends can attest, and love giving a pretty gift. My second rule of thumb is to do it as inexpensively as possible, without making it look cheap.
With wrapping paper, I try to reuse as much as possible. I've found the Sunday comic pages make great birthday wrapping, and can be recycled in the end. I love using pretty, glitzy paper at Christmas, but try to make sure that it's good quality, so that when someone unwraps the gift, if they don't want the paper, I'll quietly sneak it away, fold it neatly, and use it to wrap another gift. If it's not good quality paper, then it generally tears and can't be reused as readily. Plain brown paper, plain newsprint, butcher paper, and newspaper can be stamped or painted with your own designs and are fun for kids to make. (These generally fall into the budget arena, although the newsprint, brown paper, and newspaper are recyclable if you stamp them.) I've also found that fabric makes great wrapping "paper", although it's a little trickier to get neat folds, and is definitely in the "reusable" category. (Benny's family has been known to wrap gifts in pillow cases and sheets, or not at all. While this is definitely green and budget friendly, I just don't find this as festive--love you all!)
I ALWAYS reuse gift bags and tissue paper, sometimes to the point of being OCD about it. If I see anyone throwing away perfectly good tissue paper (i.e. it doesn't have tape all over it or hasn't been torn to shreds), I'll almost hurtle myself across the room to save the precious tissue paper. (And if it's the pretty printed stuff or gold/silver, I'm all over it. You can use gold/silver for ANY occasion!) In our family, we find that we just swap gift bags around quite a bit. Being a teacher, I'm never in short supply for gift bags and tissue paper, as students generally bring Christmas and end-of-the-year gifts in these (really, most of their moms send them, but they're still much appreciated).
My great aunt has mastered the art of wrapping without tape (I think it's a Depression era thing), so her wrapping is easy to reuse, and she saves on tape. I have yet to master this art, but want to take a few lessons the next time we see her in CA or over the holidays in NC.
For ribbon, I try to use grosgrain or wired ribbon. Although this is more expensive than curling ribbon up front, it can be reused over and over again, if you're creative. I've also found that incorporating a well placed Christmas ornament is a nice way to make a package more festive for the holidays. It doesn't take much wired ribbon to make a present look professionally wrapped, especially if you use a double-looped bow. (I'll post a play-by-play of my bow making and wrapped gifts for inspiration sometime soon.)
We cut the front off of any greeting card we receive and use it as a gift tag. Some of the most beautiful cards would be thrown away by others, but in our family, they get a second life. (We recycle the part that has been written on.) This trick works for almost any birthday, thank you, Christmas, or wedding card. (We have so many from our wedding, we'll never have to buy a wedding gift tag again!)
I also make all of our thank you notes/greeting cards from my stamp collection and card stock. Sometimes, my greeting card finds have new life in these note cards. I find this to be a great way to spend an hour or so on a Saturday and we save tons of money on greeting cards. (I am amazed that some greeting cards sell for upwards of $5.00!) I'm fortunate to have family who enjoys crafting as well, so we had an assembly line for making our wedding thank you notes in my aunt's dining room. We had 300 notes knocked out in a few hours once we got the system down.
As for green gifting, I find that it really takes knowing your recipient (which I hope you do if you're giving them a gift!). So many of our friends and family are trying to simplify their lives and teach their children not to buy into the consumerism that drives our culture. So, often, instead of giving a physical gift, we make a donation to a charity that would mean something to that family or individual. For instance, for our friends who have a child who had a cancer scare, we made a donation to the American Cancer Society for his third birthday. I'm sure that this gift meant a lot to the family and I know that the child didn't miss the gift at all... he just had a ball with his friends and loved the cupcakes. There are hundreds, thousands of charities and nonprofit organizations you can give to out there, so figure out what would mean something to your friend or family member and give away. We find that a well phrased message on a handmade note is a nice way to convey the gift we've mad in the person's honor. (On the budget side of things, the majority of these gifts are tax deductible, so when you make your donation, they will send you a receipt. Keep those receipts in a folder so they'll be handy for the next tax season.)
I hope you've picked up a few good tips today and have an occasion to try them out soon! Sharin' the green love and savings!