As stated in CrAzE's writeup above, this goes against the spirit of Christmas. If you do glean enough information to figure out your presents, remember to act surprised/excited/happy even if you aren't! You don't want to be considered an ungrateful wretch and left off of everyone's list next year.

The following details methods for non-invasive gift determination.

Normally, the wrapping paper removes our sense of sight or at least dulls it to the point of not being of much use to us. If the wrapping paper happens to be somewhat translucent, it may be possible to view a brightly colored box under bright lights when you press the paper firmly against the box. This is usually a dead give-away as to the contents.

The shape of the item can give much information. This is especially true in the case of books, calendars, modern media such as DVD's and CD's, video games and action figures (or anything in a blister pack.) All of these have fairly distinctive shapes and will allow you to match the potential gift to a requested gift on your wish list. This can even be applied to home electronics or other large toys if you are familiar with the dimensions of the box. Not too many toys come in boxes as large as some of the newer home video game consoles. Stuffed animals are also very distinctively packed and you should be warned of the danger of pressing too much into the open front, tearing the paper, and leaving evidence of tampering. Remember, being non-invasive is our goal.
By the time you have handled the item, you have an idea of its weight. This can confirm the identity of media or books. Each medium has a particular weight, complicated only by the existence of multi-disc sets. Books are very high density and will be quite heavy for their size. This is especially true for hardcovers.

Since you have the object in your hands, you can give it a shake. Be very gentle, especially with unknown lighter items. An extended relative may get you some small object d'art if they have no specific requests from you. This is a tried and true method for figuring out what has been so delicately wrapped. This can further verify media or, if you have done proper research, a particular toy. Be sure to learn the sounds the various items you are expecting will make. Most commercially produced toys are very well packaged, but many still make some sort of clatter. This is especially true of building toys. If you are a Lego fan over the age of 4 and can't recognize the sound of a Lego set being shaken, go to your nearest toy store and familiarize yourself immediately.

Many of theses methods can be made useless or less useful by procedures such as secondary packing, multi-packing, or repacking. Secondary packing involves placing the item in a larger, more uniform box, which removes information about its shape and can alter the weight slightly. An item is repacked by being removed from its original box and placed inside a different box. This can greatly complicate things, especially if the item came in a peculiar box. Also, the sounds produced when shaken can be changed quite significantly. Multi-packing is usually the easiest and most devestating technique; multiple items (usually related) are wrapped as one item. For example: CDs are placed inside a CD rack, then wrapped. Getting around this requires complete knowledge of the properties of likely gifts and a keen sense of how they will behave when combined.

I find these techniques more satisfying than the spies and razor blades method, since they require deduction rather than "seduction". They are much less dangerous since they (if done properly) will leave no evidence of tampering asides from fingerprints. Furthermore, many of these fall within the bounds of acceptable behavior. However, if parental units determine that you have become too skilled at these, you may be forbidden from handling presents before opening them. Therefore, keep your new knowledge secret from their suspicious ears.

Good luck and Happy Holidays!