Ahem.
No downloading is legal unless the owner of the copyright has given permission for you to do so.
Limewire - the software - is legal. What you do with the software, not necessarily so.
Quite frankly, it is unlikely that you are going to find pre-release tracks by "big name" bands to download for free anywhere. But... both Napster and iTunes (LEGAL download services - where you have to pay to download music) often have "Exclusives" where they preview a new album/single/whatever - that's probably your best chance.
Of course, you can always check on the artists' websites - they'll often let you know what's happening - and sometimes offer free downloads.