You can make your own or buy something simple, depending on your level of expertise and interest. The least glamorous yet highly effective treatment for window and door drafts can be resolved by taking a trip to your local hardware store. Removable foam inserts (like this one found at Home Depot) can be cut to size and neatly stuffed into the cracks of windows. Some are even designed to work while opening the windows when fresh air is needed. Under the door there are some great options that allow you to still open and close the door without having to readjust the draft stopper.
There are also more colorful options for doors and windows. These "snakes" are best for seldom used openings like the basement or attic door or windows that plan on remaining closed during the winter. Many can be found on Etsy for less than $20.00 (search for "door draft stoppers") or, if you have some leftover material you can easily make your own (here's a good tutorial).
Don't forget the other source of draft: the fireplace. Of course you shouldn't plug up the fireplace if building fires is a weekend ritual. But if you never use your fireplace, and if it doesn't have a good draft sealer, consider something like this to stop the cold air from rushing in.
Image: Flick userphotofarmer