It depends on what you want to do. If the only thing you need audio for is to play stereo sound through the speakers on your monitor, doing that via the HDMI output from your video system is OK. In some set-ups (depends on your video card) the audio signal may have the option for more sophisticated signals on the HDMI cable, but that would require an external audio amplifier and speaker system.
In either case, video cards rarely have any way to connect an external audio source to an input. If you want to record audio input from an external source, or if you will be using a microphone that must plug into an input jack, you'll need more than what the video card has. Likewise, if you plan to output more than 2-channel stereo (e.g., 5.1 surround sound) either as analog signals or digital (electronic or optical cable) to speakers or an amplifier, those rarely come on a video card. And just for clarification, these days most video cards come with their own audio output chip on them, exactly for the purpose of making audio available on the HDMI cable. Virtually no video cards have a way to allow input of an audio output from a mobo or sound card into the video card for a simple pass-through system.
As others have said, though, an audio chip and output system is almost always included in a mobo these days, so this may be a non-issue.