Is there a "Select by Attributes" plugin/widget for ArcGIS Server JS API?

If you are using ArcServer 10.1 you could create a Geoprocessing service which references either a model or script that you built to do this.

The link above gives step by step instructions on how to create the model, then create the services and finally consume it in your app.

Alternatively, there is this sample that uses a query to select records, you could modify that to allow for multiple services.

A couple of years later, I was looking for exactly the same thing as the OP. This question shows up in the top results of a search engine, so I decided to leave this update here as a reference.

In the Summer of 2015, Esri has released a Select by Attributes Widget in their GitHub repository.

This widget attempts to recreate ArcMap's select by attributes tool as accurately as possible within a JavaScript application. This widget only works with feature layers and these must be passed to the widget's constructor as an array.

Live Sample