During past visits to New Orleans, I passed up Cafe du Monde because I was put off by the constant, massive crowd. During my last visit, however, I finally got brave, and battled the crowd for a table, and was rewarded with delicious coffee and excellent beignets.
For first time visitors, you should be aware that you seat yourself, so you have to be quick, when you seen an open table. There is limited indoor seating, and it seemed, to me, that there were more open tables inside, because folks just grab the first table they see, outside. Go when you have plenty of time, because it takes a while for the servers to make their way to you. If you're interested in buying a can of Cafe Du Monde coffee, to take home, it's available all over town, and at the airport gift shop, but it's significantly cheaper at the cafe (about $6.50 per can). If you get it anywhere else you'll pay $1 - $3 more for the same product.