It is not illegal to download from Limewire. Limeware is a piece of software that hooks into the decentralized Gnutella peer-to-peer network, made of millions of other computers sharing files. Limeware does not host any of the files on the Gnutella network; it is merely a portal that allows you to search for any type of content you wish.
While using the application itself is not inherently illegal, the legality issue arises when it comes to the content downloaded via Limewire. Just as the original Napster before it, Limewire is a hotbed of people distributing content they do not hold the copyright to, and the amount of illegal shared content on this network is enormous. A search for any artist name returns hundreds of files, but chances are this artist's record label and management did not upload these files for free legal transfer amongst these millions of peers. There are cases these days where the artists or even directors are releasing their original content free of charge and freely distributed through the various online channels, but such cases are far from the norm. Limewire tries to combat this known and obvious use of their application by asking the user whether or not they might use the program for copyright infringement, and an answer of "yes" yields a message saying that Limewire does not distribute the program to people who intend to use it for purposes of copyright infringement, and all subsequent downloads fail. Though some simply select "no" unscrupulously, and download away.
The legality of the use of Limewire comes down to the intent of the user. The temptation is certainly there, much like a bicycle left in the front yard of a neighbor's house. The bike does not belong to you, and if the bike was in the backyard or in the garage, the thought to take the bike would never cross one's mind, but sitting in the front yard unguarded to the temptation is much stronger. Limewire, while intentional or not, takes that bicycle out of the garage and lays it unguarded on the front lawn. It's a fairly safe bet to say that many Limewire users intend to obtain illegally shared files.
Aware of this image and hoping to turn a new leaf, Limewire opened the Limewire Store, an online shop for legally purchasing DRM-free music files. It's a common occurrence for such peer-to-peer programs to sell legal music files to avoid the flack received from the illegal use of the program.
The best bet is to avoid use of the Limewire program unless one specifically knows the owner of a particular file or owns the file herself. The recording and motion picture industries have been coming down hard on illegal file shares over the last few years, and the easiest way to avoid such legal trouble is to completely remove the temptation.