It is a standard that all text links follow an identifying convention. This can be your choice of any styling combinations, but generally speaking, they should all follow suit.
An exception would be navigation elements. Some sites that use huge text-footer areas don't have to follow these conventions exactly for quasi-sitemap links. Most still share elements (a darker/lighter a:hover, an underline of some sort, etc).
Here's a pretty good article from Smashing Magazine that talks about web standards for styling links.
Essentially, you want to make your links as readable as possible. Users scan content for links - they do not investigate each word to see whether or not it's a link. This is why having a uniform style convention all links follow is important. When a user identifies "what a link looks like", they can depend on this description in all future instances - except for blatant "links", such as a UI Button.
By having multiple co-existing styles for text links, you run a risk of confusing the user a to what links should look like on your site, and possibly cause them to miss out on content they wanted due to a confusing link styling system.
This is also why establishing a style guide is important - to keep uniform sense and logic throughout the design process, and to create design cohesion.