This is actually exactly what happened with MtGox. A bitcoin wallet is two codes: the public key, which is 30 digits, and the private key which is 50. The private key is how you retrieve the funds. I don't know about coinbase specifically but I would check what backups they have so that you can still get your private key even if the website was down. What happened with MtGox is people trusted MtGox with their private keys, and though incompetence of malice MtGox lost the private keys, and there were no backups, so those bitcoins are now gone forever.

I personally am a bit suspicious of web wallets. I don't keep bitcoin in them I just use them as receiving addresses, before moving the bitcoins to a different address such as a paper wallet. Paper wallets are where you print the private keys out on paper, and then put that bit of paper in a safe or something. That way the only way they can be stolen is if someone gets that bit of paper (or lost if the paper is destroyed).

You can have as many wallets as you want and they come in all different forms; web wallets like Coinbase, smartphone app wallets, desktop clients, paper wallets etc. and there are advantages and disadvantages to each.

My advice would be to use a web wallet or phone app wallet as petty cash, and only hold small amounts in there, or only use it for sending and receiving funds and keep no bitcoin in it for any length of time, and look into paper wallets (there are youtube tutorials on this) and other "cold storage" options for long term secure holding of larger amounts of bitcoin.

So I just started a Coinbase account a moment ago, and they provided me a Bitcoin address. My question is, if Coinbase disappeared how would I access my money that is on my coinbase address?

Are you able to use your bitcoin address with other wallet sites?

I'm a bit confused... But basically my issue is, I don't want to have money locked into an account that could disappear, or I could possibly lose access too.

Thank you to anyone that helps!