Are Vector Images still popular?
A simple answer … Yes Yes and a thousand times.
Everybody needs a vector. All top quality products that you see are using vectors every day. The game you see , the apps you use , the products you buy all uses vector images.
For a Game developer , to maintain the quality of the images across all screen , the designer need to design the images in Vector format. To print a design on a Tshirt , images need to be of same quality no matter what the size of TShirt is. The images that you see you TShirts on sites like Zazzle or Cafepress are designed as Vectors.
So, start learning about Vectors. You can see the basics of Vector here
See a sample fresh vector here. The vector can be downloaded for free at http://smartvectorpics.com/backgrounds-and-textures/blue-yellow-green-patterned-hearts-as-cards/