this Block Chain is replicated and stored on every user's computer (is that correct??). And when I installed Bitcoin for the first time, it took many hours to download the Block Chain - which seems to corroborate with how I understand it...
There are many Bitcoin clients. The "official" Bitcoin client (Bitcoin-qt) is not really official, and there are clients out there which already provide comparable features without requiring you download the blockchain - so no, not everyone needs to download the blockchain to use Bitcoin. It's not necessary to wait hours or days to be able use Bitcoin after installing, and these thin/light clients require only an insignificant amount of computer resources. A fix may be unnecessary (though it would be ideal) while servers can host the blockchain.
Aside from e-wallets (blockchain.info is usually fairly highly-regarded), there are clients such as
Electrum for your desktop computer, and clients such as BitcoinJ and Bitcoin Spinner for Android. There are more if you look, but these are the services/clients I hear the most about. With the exception of e-wallets (in all cases I'm aware of), all these lite clients do not store your private keys on a central server, so you are at no risk of losing coins if one of these services are hacked.
Cheers!