Answer:
There is a Basic Membership for Moshi Monsters which is free, but you will not be able to do all the activities or catch all the Moshlings. With a Basic Membership, you can get all of the moshlings except the ones that need a Snap Apple, a Crazy Daisy, or that are part of a Super Moshi Mission, or that need a Limited Edition Code for a specific seed. You can keep 2 moshlings in your house and keep one moshling in your backyard.
To get the free Basic Membership, go to moshimonsters.com, click on the link at the top which says 'Membership'. There is a sentence at the top of the page that says: The basic version of Moshi Monsters is free (sign-up here). Click on the 'sign-up here' to get a free Basic Membership.