You can leave it at that, but you'll have more grapes and less disease problems if you prune it right- which can mean removing up to 80% of the plant!
Pruning helps the vine get the light it needs, better airflow (which reduces disease), increases production, and gives you a better-looking plant. See the video below to watch how to prune properly.
For those of you who like to see the science and details behind it, check out this very good slide show about it. This one is targeted at commercial grape growers, but includes a lot of practical information for the average gardener.
Or read this short pruning summary- less than 2 minutes to read- including categories of grapes. I discovered from this one that my Niagara grapevine, being less vigorous than many, should have 3 buds left on each spur (stub left on the main vine), rather than the 2 shown in the video below.
If you'd like to learn about all kinds of pruning for fruiting vines, shrubs, and trees, try the USU Extension Pruning handbook. I have a hard copy of this same handout from when I took the Master Gardener course in about 1999. I pull the booklet out almost every year and learn more each time. The more I've pruned, the more I understand all of it...