Yes, there are several server-side web frameworks for Dart. See the list below:
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Aqueduct – Dart HTTP server framework for building REST APIs. Includes PostgreSQL ORM and OAuth2 provider.
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Start – Sinatra-inspired web framework to serve static files, handle dynamic requests, web sockets and create JSON responses.
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Angel – A server-side framework designed for full-stack development, with an emphasis on code sharing, scalability, and a low learning curve.
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Redstone – A metadata-driven microframework.
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Stream – Lightweight web server with request routing, filtering, template engine, WebSocket, MVC design pattern, and file-based static resources.
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Express – A simple, thin expressjs inspired layer around Dart’s primitive HttpServer APIs.
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Shelf – Shelf makes it easy to create and compose web servers and parts of web servers.
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Jaguar – A server-side framework built for speed, simplicity, and extensibility.
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Force – A real-time web framework, embracing web sockets, making communication even better.
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Vane – A framework with built-in server runtime environment and middleware system.
See also this list.
Furthermore, there are a few Dart packages you can use to create your own server-side web framework.
For templating, there are two mustache libraries on pub, mustache and mustache4dart.
For URL routing, see the route package.
There are packages for databases, mysql, postgresql, and mongodb and couchbase.
For caching, see memcached.
I haven’t seen any session management packages, you’ll probably have to roll your own and persist session data using a database.