When opening and old wallet created by simplewallet, I'm asked for a fee to import old transactions, why?
To add to what Jolly Mort correctly said (rescanning the blockchain is a heavy process on the server, which the Mymonero operators want to discouraged), it is possible to have a wallet created in Mymonero, then import it in simplewallet. This will not incur a fee in Mymonero, and you will have a wallet which you can use in both.
See for instance If I saved my view key and spend key can I recover my wallet if my mnemonic seed is lost? for instructions on how to import a wallet from keys with simplewallet (Mymonero will show you the keys to your address).
Re-scanning the blockchain from 0 consumes server resources and takes time. The fee is there to discourage this use case, but providing the utility if it's really required for some users.
If a new wallet is generated, the server doesn't need to re-scan the blockchain as it knows that the wallet has not been used before.
The answer from user36303 was correct at the time but is no longer up to date. Following the large rise in XMR prices a few months back fluffypony lowered the import fee from 10XMR to 1XMR. The following message is now displayed on MyMonero.com when attempting to import old transactions:
Import your transactions from the entire blockchain
To import all your previous transactions and account balance you have to pay a once-off import fee of 1 XMR to the account listed below. The command to make the payment has already been prepared to make it easy for you to copy and paste it into simplewallet.
What you are seeing is the Import Instructions modal.
IF you didn't create a fresh wallet with MyMonero but you imported an already-created one (like from the GUI) by using your:
(a) mnemonic seed, or (b) address and keys,
then you can send MyMonero a small fee in order to subsidize the MyMonero back-end (server / hosting) doing the very computationally expensive job of scanning the entire blockchain for your account transaction background and balance.