I'd say it depends on the design of your website. Personally, I do allow some of my links to be underline mostly for usability purposes but don't go out of my way to do so if it go against my site design or some other styling just looks better. People are used to seeing links underlined and whilst most of us Internet users can tell a link a mile away, some users may not.
You can have the link with different color on hover if you don't want different color then you can have it as underline, there needs to be any one differentiate for links and normal text.