Can a virus spread through my Linksys Router to my other computers?

If the computers are on the same network, and the virus spreads by probing other systems, yes it can spread over the network.

However, if other PCs have good firewalls, they would block most of those attempts, except those that have file sharing open.

Yes, it is possible, and the router has little to do with it. Some forms of malware known as worms send themselves over networks, either through a full network with a router, or over a single-connection network with an Ethernet cable.

Make sure you have good firewalls up and running on all computers on your network at all times.

Good luck.

the router in itself is a firewall, but if it has added protection, why would you not use it?? of course viruses AND hackers can access both computers on the same nertwork, as long as they can get past the router first,, that is the point you want to stop intrusuions at!

if the comp is not shared then no but if it shares file and the virus is a retro worn or a stick it might but trojans and stuff like that no... if it has a virus dont connect it to ur network i suggest (if u dont know much)

A computer that is known to be infected should not be directly connected to your network. Clean it first (ie: use a bootable, up-to-date antivirus disk or USB drive).