Yes. And it should vent to the exterior. It'll help keep your kitchen clean and safe.

halcyonbear is absolutely correct.

The vent is there for a very good reason. Yes it takes up space, and it also keeps airborne matter from both your cook top and oven vented to the outside. There are lots of low profile options available which take up very little space. There are also microwave / hood combinations, which are bulkier, but serve a dual purpose.

Do a really pretty stove hood. They can add so much character and charm to a kitchen.