Yes
Gary,
Most hosts that support PHP and MySQL will run osCommerce.
Some hosts, who use the cPanel for end-users support automatic osCommerce installation using the Add-On Script icon. Another thing to look for is a shared SSL certificate, to enable the check-out security features in osCommerce.
My company specializes in eCommerce development and hosting using osCommerce. We are one of 52 official Canada Post eCommerce Solution Providers in Canada.
Please contact me: http://listbay.ca/eStore
Ben Blakley
"Customizing the PayPal Gateway"
http://ListBay.ca/eStore/us.html