"Must Have" is always going to be a little subjective, based on your interests and what you plan on doing with your iPad. But here goes my list:
1) Flipboard (Free) online news reader/aggregator. It picks stories from around the web based on your interests Twitter and Facebook contacts. Fantastic implementation.
2) Pages ($9.99) from Apple. If you ever need to write something longer than a paragraph or two, its sort of nice to have a word processor, rather than relying on a notepad. Its still a little creaky printing, unless you have one of the ePrint HP printers. But a well made App.
3) Remote (Free) from Apple. Control iTunes on your computer, AppleTV, or iPod touch using the iPad (or touch) as a graphical remote control.
4) Netflix (Free) Obviously, you only need this is you have a Netflix account. Watch streaming movies and TV in bed, in the garage, in the bathroom.....
5) The Weather Channel Max: (Free) Better, faster, and more useful than EITHER the Weather Channel website or even the cable channel. (No waiting around for "local on the eights") I actually found the Weather Channel App gave better, more reliable forcasts than the local media when I was in EUROPE last winter.
6) Speedtest XHD (free): Wondering how good your DSL or cable internet is? This free and easy utility checks upload and download times.
7) New York Times for iPad (free for now): The best newspaper in the world, free, in a well-designed, well-implemented, no-nonsense App. Saves stories for reading offline.
8) TED: (free) Fascinating video talks by some of the amrtest, most interesting people in the world, on a variety of topics. Talks range from just a couple of minutes to a half hour or so. Browsable and searchable.
9) Epicurious (free): Recipe collection covering just about anything you are likely to cook. Combine with a stand in your kitchen, and you have a cookbook whose pages never get stained with flying spaghetti sauce.
10) Pandora (free - premium available): Internet music at its best Create a station that plays just the music you like.
11) Whats On? (free): Local TV and cable (and movie) listings. Hate having to page through the clunky onscreen program guide on your TV? This App provides the same data, in a customizable App that you can browse from your couch, without interupting whats on the TV. Can program it to send you alerts so you don't miss the next episode of Top Gear.
12) ESPN ScoreCenter XL (free): Keep track of your favorite sports and teams. Scores, highlights, plus upcoming game times.
13) Garageband for iPad ($4.99) from Apple: If you have ANY interest or talent for making music, this is a fantastic App. As good as it is for making music - its even better at showing what a fantastic device the iPad is.
14) GT Racing Motor Academy ($4.99) Gameloft: One of the best racing games out there. The perfect (IMHO) mix of thrills, skills, realism, and gameplay.
15) Sketchbook Pro for iPad ($7.99) AutoDesk: A pro-level drawing and painting tool. With layers, custom brushes, colors, text editing - perfect for creating new images, fixing photos.