I was complete shit at gift-wrapping until I watched some YouTube videos on it a couple of years ago, and now I’m only partially shit at it.
Here’s one for you to look at: http://www.youtube.com/watch?v=5Wp2dxIAocI
I’m glad I took up origami in high school, as I had to wrap one of these oblong gift boxes this year. They come with a hinged cardboard lid (attached at the top-left side) that folds right in place, so it’s a solid surface to wrap over, but those angles are scary.
The shop owner said occasionally people will ask if he could put a ribbon around it. I’m hoping there haven’t been too many who’ve needed the physics demonstration on why that might not be practical.
Oh, I nearly forgot, lately I’ve been interested in Japanese style fabric gift wrapping. Furoshiki looks very interesting, but I’m not sure that I want to invest in all those fabric wraps. It was tricky enough to tell people that they should save the boxes and bags for re-use, rather than throw them away.
I know you didn’t want tips but…
Try not using tape. Bind the wrapped present with string or ribbon instead. I didn’t use tape until my niece and nephew came along.
Another tip is to double-wrap the present. Use brown paper for the inner wrapping. This will make your outer wrapping less likely to tear as you wrap around a softer surface.
Every couple of years I like to tape up all of the seams. It’s fun watching the victim trying to find a place to start. 
Used to be a cruddy wrapper. Then one day quite a few years ago I wrote a program (one version for a PC and another version for a RPN Hewlett Packard calculator, that calculates the exact dimensions of the wrapping paper needed. The input is the height, width, and length of the box, and it comes out perfect every time. My wife thinks I’m nuts, but I can wrap a package now as good as she can!
I’m thinking you could make a fortune selling that to geeks around the world. 
I took gift wrapping in 4H back in the day. I’m the queen of pretty packages in my family. 
For the oddly shaped packages, get creative with the wrap and ribbon. For boxes, the tips previously posted should get you through it.
Once upon a time, an office I worked in had a Xmas party with a gift Xchange. One lady had spent a year or more trying to update (re-write, really) our product’s user manual. It grew to such a monster project that the whole office was involved one way or another. She must have wasted a few forests printing out drafts of various chapters.
So I grabbed a handful of drafts from the wastebasket, took them home, and cut them into a bunch of irregular-shaped pieces, and then taped them all together to make a crazy-quilt. Then I used that as wrapping paper for the gift.
The product was a software app that “turns your PC into a cash register”. We had piles and piles of receipt-printer output laying around (because I was doing a lot of testing of that at the time). So I took a length of that and made bow of it for the package.
That’s how I wrapped a Xmas gift once.
Everyone got a good laugh out of that.
That’s why guys need/have wives. That’s what they’re for.
One way I’ve wrapped gifts like books is to wrap them once in aluminum foil, then a second time in one of the colored plastic wraps (they tend to come out around the holidays–things like Cling Wrap), then tie a ribbon around them. They look pretty, colorful, and metallic. And it’s pretty easy.
Don’t feel bad, I can’t wrap either!
I’m going to wrap some presents this week, would it benefit anyone to make a YouTube video of my method (the one I learned by watching the wrapping people at the mall)? It wouldn’t be too much effort as I could just borrow my son’s FlipVideo camera. Yes, helpful? No, not worth it? You tell me. If there is interest I will do it.
My little secret is to use Hallmark wrapping paper.* Their paper is fairly thick so you get a good fold but the most important feature…
…there is a grid on the back of the paper. So, you can easily cut in a straight line and centre your gift perfectly before taping.
Also, don’t use too much paper. For the width, Use just enough to cover all four sides of the box plus a quarter of the size of the longest side more. For the length, use enough for the long side plus the end you are wrapping plus a quarter more.
I also use a piece of tape for every fold (carefully hidden under the next).
And if it is not in a box, go buy a box. Oddly shaped items almost always look like crap.
I have it down to a science. This year, I had 40 boxes to wrap and it took me about 3 hours (4 if you include ribboning and labelling). My husband says I should volunteer at the charity gift wrap place in the mall next year.
*I am in no way related to, or being paid by Hallmark.
I don’t wrap gifts. I’ve done the gifty bag things, that are all fancy, but I just don’t give gifts for the “Holidays” to friends and family as a ritual. Often when I see them, just give them something person to person and say “thought you’d like this.”
Wrapping isn’t tough, though – I did it when a kid for various family members. Just fold the ends and into little triangles and use some tape and then the bows and ribbons. And a little cardlet attached is good.