1- Check if the system is up in the network. Telnet/Ping the server.
2- Check if the date/time match between the server and the client machines.
3- Change the service account of sqlserver and check if the error is resolved.
4- Refresh the dns on the client.
5- Check windows event log for advanced details of the error

Below links give additional details:

http://support.microsoft.com/kb/811889

http://support.microsoft.com/kb/319723

[xml]
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Cannot connect to server name.

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Cannot generate SSPI context. (.Net SqlClient Data Provider)

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For help, click: http://go.microsoft.com/fwlink?ProdName=Microsoft+SQL+Server&EvtSrc=MSSQLServer&EvtID=0&LinkId=20476

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Server Name: server name
Error Number: 0
Severity: 11
State: 0
Procedure: GenClientContext

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Program Location:

at System.Data.SqlClient.SqlInternalConnection.OnError(SqlException exception, Boolean breakConnection)
at System.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj)
at System.Data.SqlClient.TdsParser.SSPIError(String error, String procedure)
at System.Data.SqlClient.TdsParser.SNISSPIData(Byte[] receivedBuff, UInt32 receivedLength, Byte[] sendBuff, UInt32& sendLength)
at System.Data.SqlClient.TdsParser.ProcessSSPI(Int32 receivedLength)
at System.Data.SqlClient.TdsParser.Run(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj)
at System.Data.SqlClient.SqlInternalConnectionTds.CompleteLogin(Boolean enlistOK)
at System.Data.SqlClient.SqlInternalConnectionTds.AttemptOneLogin(ServerInfo serverInfo, String newPassword, Boolean ignoreSniOpenTimeout, Int64 timerExpire, SqlConnection owningObject)
at System.Data.SqlClient.SqlInternalConnectionTds.LoginNoFailover(String host, String newPassword, Boolean redirectedUserInstance, SqlConnection owningObject, SqlConnectionString connectionOptions, Int64 timerStart)
at System.Data.SqlClient.SqlInternalConnectionTds.OpenLoginEnlist(SqlConnection owningObject, SqlConnectionString connectionOptions, String newPassword, Boolean redirectedUserInstance)
at System.Data.SqlClient.SqlInternalConnectionTds..ctor(DbConnectionPoolIdentity identity, SqlConnectionString connectionOptions, Object providerInfo, String newPassword, SqlConnection owningObject, Boolean redirectedUserInstance)
at System.Data.SqlClient.SqlConnectionFactory.CreateConnection(DbConnectionOptions options, Object poolGroupProviderInfo, DbConnectionPool pool, DbConnection owningConnection)
at System.Data.ProviderBase.DbConnectionFactory.CreateNonPooledConnection(DbConnection owningConnection, DbConnectionPoolGroup poolGroup)
at System.Data.ProviderBase.DbConnectionFactory.GetConnection(DbConnection owningConnection)
at System.Data.ProviderBase.DbConnectionClosed.OpenConnection(DbConnection outerConnection, DbConnectionFactory connectionFactory)
at System.Data.SqlClient.SqlConnection.Open()
at Microsoft.SqlServer.Management.UI.ConnectionDlg.Connector.ConnectorThread()
[/xml]