On a recent trip
(which included Hong Kong Disneyland) I planned for 400 pictures a day and actually came close (about 8000 pictures over 3 weeks). Now many will be deleted (not quite sharp enough, bad composition, too dark or too light, etc.)
I brought enough memory cards (almost two dozen) to shoot at maximum resolution and quality all the time.
You need to check your camera settings every now and then to be sure you did not accidentally lower the megapixel rating with incorrect button pushing. If you shoot at lower megapixels, you cannot reclaim the quality of higher megapixels after uploading to your computer or at the store photo kiosk. I have read horror stories here on The DIS about people who accidentally had their camera set to "thumbnail" or "VGA" or "wallet" which are among the lowest rsolution settings selectable.
Work with number of pictures per day first, then figure out the number of memory cards. Number of pictures per memory cards is estimated in your camera instruction manual. The number of pictures per memory card will vary a little depending on the content of the pictures but ignore this for the purposes of figuring number of cards needed. Pictures with large amounts of solid color whether shadows at night or clear sky during the day, take up less memory space. Note that you do not compute number of pictures by dividing the memory card size by the camera megapixel rating, for example 2GB card holds 200 pictures from a 10MP camera is not a rule of thumb.
That said, I do use lower megapixels for pictures such as eBay pictures that will never be viewed at more than say 1000x1000 pixels. And, something is better than nothing. If you are far from civilization (a town with a store that sells cameras) and running short on memory cards, you may have to resort to things like 3MP.
Yes, you can mix resolutions on a card, for example
in a pinch delete an unwanted higher resolution picture to make room for two lower resolution pictures.
Digital camera hints:
http://www.cockam.com/digicam.htm