You are not required to register on a website that hosts Bitcoin wallets (always make sure that these sites are reliable!). You can also run your Bitcoin wallet on your local computer. Note that this is also risky in the sense that if you forget your password, and have no means to recover your password, then your Bitcoins are forever lost.
This is easily fixed by writing down, or preferably memorizing, your recovery tokens. In the case of Electrum, the program requires you to memorize (or write down) a list of 10+ items, which is used to recover your password. In my case, I have no more than 0.003 bitcoins (this is equal to around $20 right now) in my wallet, so even if a burglar invaded my house and retrieved my carefully hidden paper with my recovery tokens, then my loss is still minimal. I recently spent it on ACR, though.