The title says it all - vector, raster, geoprocessing plugins?
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There are so many, but the top ones for me are:
Atlas - Only been available for a couple of weeks but use it all the time since. Allows you to create map books easily. Saved me a lot of time on a project with a pipeline split into 20 maps - all I had to do was provide the plugin with a layer of polygons for the locations of each map and a composer and it automatically turns each composer into an image file.
Numerical Digitise - Allows you to provide coordinates to create features. Very useful for creating a point at an exact coordinate quickly when someone gives me a site location rather than trying to click in the right location on the map.
Time manager - Allows you to view data which has a time element to it. We use it to visualise ecological data over the course of a survey - looking to see if there are any parts of a study site that have more data at certain times of the survey period and where and when the most data occurs.
Memory Layer (and memory layer saver) - like the cosmetic layer in MapInfo - really good for creating a quick object that you do not want to save to a shapefile/database.
Import project - Allows you to load in layers from another project - you can choose which ones you would like to load. I find it very useful to set up a project with all of my base layers loaded and styled (like Ordnance Survey mapping, site boundaries, buffers etc), and then import these using this plugin when I am ready to incorporate them with other data.
XY tools - Allows you to load a excel/openoffice/libreoffice file as a point layer if it has coordinates in it, and also allows you to export data to the same formats. Very useful for exporting data for reports.
Ordnance Survey Translator - Imports OS MasterMap data from .gml format. Can then be styled using the styles from this website: http://www.lutraconsulting.co.uk/resources/ostranslator.
Photo2Shape - extracts georeferencing information from geotagged images. Great if you have a camera with a GPS built in for visualising the image locations in QGIS. It allows us to visualise where photos were taken on a project site so people can remember where they were when they took the photo.
Table manager - allows you to manage a tables structure (rename, insert and delete columns etc).
Shapefile splitter - can split a shapefile into separate files by the values in a column. We use this when we need to provide people with shapefiles that only contain one feature type.
Hard to say, they are many (more than 200 if you consider both core and contributed plugins).
Among the ones available out of the box: ftools, gdal tools, georeferencer, delimited text layer
Contributed: Database Manager, Value Tool (if you do raster analysis), Easy Print (for mapbooks) and many more...
PostGIS Manager is a must if you use PostGIS. Also, I like the Interpolation plugin, and OpenLayers is good for quick maps.
It's more of a housekeeping plugin, but Zip Layers is essential for me. I use it in two ways:
The plugin creates individual zip files containing a shape file of each of the layers you select. CRS and metadata is kept intact.
It's not currently in the official repository, but can be found at http://pyqgis.org/repo/contributed
For me, Openlayers plugin is the most used plugin.
Apart from the easy-to-add background of Openstreetmap or Google satellite just to check if a layer with an exotic CRS is well-placed, I have managed to cut some geotiffs with official maps into tiles, and have them delivered by an apache localhost.
This needs some tweaking in the openlayers plugin code (unfortunately after every update of the plugin again), but gives me a wide choice of map backgrounds even when being offline and thus having no WMS service at hand.
GPS Tools I also use frequently to add waypoints taken outdoor to my local databases.
Finally, Table Manager is a good tool to add and delete fields before adding the data to the spatialite databases I created.
I Use these,
SEXTANTE A large collection of tools, for most of the analysis requirement. (Now it is called processing)
Quick Finder￼ Quickly find features base on their ID or other fields.
OpenLayers If you are working with wgs84 system. This can give you a basemap. This makes it easier to perform operations and visualize results.
OGR2Layers This creates a HTML file of the map which can be shared to the website.
Transformation Tools This is very useful if you are working with undefined CRS. or you need to use special parameters for transformation.
QGIS Cloud Let's you publish your data on web, so that it can be accessed from everywhere.
Plain Geometry Editor￼ Edit geometry of features using plain text (WKT, WKB)
OSMEditorRemoteControl OSM uses different data formats than normal gis. Due to this existing data editors cannot/shouldnot be used to edit the data. Instead it will transfer the editing to the well known OSM editor such as JOSM.