Regardless of whether the new rules will be better or worse than 3.5--which remains to be seen, after all--I am still furious about paying a monthly fee to get additional material. Since they likened it to buying "a special edition DVD" over an "ordinary one" of your favourite movie, I am anxious about how much better the "special edition" will be over the normal rules. If it contains only a few "teasers", "trailers" and other lame stuff, I can't be bothered. But if it's the real deal with copious amounts of "extra footage" and in-depth "behind the scenes" material I will feel cheated. It might build a tiered gamer structure, with 2nd class citizens left out of the interesting stuff.
From what I understand, the online content will consist of three main things. The first is the content that both Dragon and Dungeon magazine used to have. The second is a virtual tabletop for gaming with people. This virtual tabletop will consist of dungeon mapping features, the ability to share maps/dungeons, and a way to make virtual minis. Third, you'll get access to online versions of the books you own that are updated automatically as errata comes in.
I think the current plan is to have much of the D&D Insider content collected into physical products. For example, the "best" of the new classes, races, monsters, and rules will probably be included in the yearly installments of the PHB, MM, or DMG (for example, gnomes or goblins will probably first appear as PC races in D&D Insider, then be published in the PHB 2). So even if you don't subscribe to D&D Insider I think you'll be able to get some of it eventually. But you'll have to wait for the book to be published.
WotC has also said they will continue to have free sections of their website, much like the previews and "Characters with Class" articles they have now.