Downloading the program, no.
What you download, yes.
In a nutshell, it allows data transfer between several networks.
You get data from on person and vice versa. There are limitations (how fast you can transfer data) on Limewire (free version), and the paid for one relinquishes these taxes.
People can only "take" called download on their end, or upload on your end, if you share the file. So do not have access to your whole computer.
Make sure you have a good firewall because this program opens your computer up to intruders (hackers).
And a good Anti-virus program, because you will get viruses.