How to create an unsortable Field with multiple values? When a CCK field accepts more than one value, the widget will display a sortable table (usually with those cross-shaped handlers); this is the default behavior. I would rather have a non-sortable widget, since the order doesn't really matter. I hope this will avoid the usage of a table element, as well.

How can I achieve this? Do I need to use hook_form_alter()?
I think you'll need to create your own module for this. Instead of using hook_form_alter(), I'd suggest doing things the "cck way". CCK provides hooks which allow modules to provide custom widgets for CCK fields. You can create a module to provide a new Widget option for multi-value fields that doesn't use an HTML table, and doesn't allow for reordering. There's a great article on Lullabot about this. It also talks about creating your own fields and formatters, but you can skip down to the widget part at the end. The sample code is very well documented and should help you understand what's happening. At the very least this will be a great starting point. If something in the article doesn't make sense, feel free to ask for clarifications and I'll add what I can.