Quickly browsing of features for the active vector layer?

This functionality is now integrated in QGIS 3.10 (not sure about previous versions):

1. Open the attribute table of the vector layer in question.
2. Click on the Switch to form view icon on the bottom right of the attribute table.
3. On the bottom left, just below the list of features, choose to either
   • Automatically pan to the current feature or
   • Automatically zoom to the current feature.
4. (Optionally activate the Highlight current feature on map option.)
5. You can then either click on the feature of interest or click on the left/right arrow to browse through the features.

Alternatively you can now also setup a keyboard shortcut (go to Settings > Keyboard Shortcuts...) to Edit previous/next feature in attribute table (respectively Ctrl+Alt+[ and Ctrl+Alt+] by default on my system).

You may also want to use the Dock Attribute Table option for convenience.

One method is to download the selenext plugin from the menubar:

Plugins > Manage and Install Plugins...

Once download, modify the selenext.py file by replacing the following in both the run() and runPrevious() functions:

box = vlayer.boundingBoxOfSelected()
self.iface.mapCanvas().setExtent(box)
self.iface.mapCanvas().refresh()

with:

self.iface.actionPanToSelected().trigger()

Reload the plugin. Now whenever you click on the the next or previous icons, the canvas will pan to the selected feature: