The original question was about the alternative bitcoin wallet called electrum. The answers given by me and other members cannot be translated to most other wallets.
If you need to know the answer to your question, you'll have to find the support thread for your wallet (since you're talking about ETH, i assume you're using mist?). Anyways, as a first part of an answer: if you write down PUBLIC addresses, i can assure you that you won't be able to restore your wallet... writing down addresses or public keys is not sufficient for backup purposes.