For those with an Arcade or the Core, you should be eligible for a memory upgrade from Microsoft. Link
Essentially you have to have an Arcade or Core console with no Hard Drive attached to it. This offer is not valid for Pro or Elite owners. The offer is either
A Refurbished 20GB HDD for $19.99 or
A Refurbished 20GB HDD + 3 Months of Xbox Live Gold for $29.99 or
A Free 512MB Memory Card (only US)
This is the solution Microsoft found to accommodate everyone in the New Xbox Experience. Getting at least the free memory card seems like a no-brainer.