Using VSTS on a daily basis I find that I add a regular list of VSTS Marketplace extensions to my VSTS environment. I find them convenient and helping me to get the most out of VSTS. The list below is primarily focussed on the Work and Code area and not so much on the Build and Release area.
The list below, in random order, lists the extensions and adds a short description and provides a link to the VSTS Marketplace . Not all items are free at this point in time, or are currently in development.
Code Search, this extension allows you to search your code repositories better https://marketplace.visualstudio.com/items?itemName=ms.vss-code-search
Work Item Search, enable rich work item search in your project https://marketplace.visualstudio.com/items?itemName=ms.vss-workitem-search
Open in Excel, open a query using Excel, what more can i say about this https://marketplace.visualstudio.com/items?itemName=blueprint.vsts-open-work-items-in-excel
Delivery Plans, useful to get insights in your delivery https://marketplace.visualstudio.com/items?itemName=ms.vss-plans
Agile Cards, need cards on paper? this extension may be really helpful https://marketplace.visualstudio.com/items?itemName=spartez.agile-cards
Package Management, allows for feeds to manage your own packages https://marketplace.visualstudio.com/items?itemName=ms.feed
Personas, identify personas for your work items https://marketplace.visualstudio.com/items?itemName=agile-extensions.personas
Product Vision, Every company or team needs a sharp product vision, make sure yours is know and seen! https://marketplace.visualstudio.com/items?itemName=agile-extensions.product-vision
Multi value Control, when you have the need for a multi-select field customize your work items with this extension. A blogpost on this is coming soon. https://marketplace.visualstudio.com/items?itemName=ms-devlabs.vsts-extensions-multivalue-control
Folder Management, when using TFVC as source control, this extension allows you to quickly work against the repository without the need of setting up a local workspace with Visual Studio. https://marketplace.visualstudio.com/items?itemName=ms-devlabs.FolderManagement
Workitem Visualization, whats in a name, it allows you to visualize your work items and relations https://marketplace.visualstudio.com/items?itemName=ms-devlabs.WorkItemVisualization
Area Dependencies, identify and visualize cross team dependencies between workitems https://marketplace.visualstudio.com/items?itemName=ms-devlabs.ShowAreaPathDependencies
Wiki, no explanation needed I hope, be aware this extension is currently still a bit experimental in its usage, but there is a high potential for it https://marketplace.visualstudio.com/items?itemName=ms-devlabs.wiki
Estimate, a nice and collaborative way of estimating work items, this works really well for distributed teams, https://marketplace.visualstudio.com/items?itemName=ms-devlabs.estimate
Enjoy!