Does MSSQL Server have the equivalent of MySQL's query logs?

SQL server keeps statistical information about all queries in various tables. You can use the following code to determine what the longest running query is (from the sys.dm_exec_query_stats table).

You should run the following DBCC commands:

This DBCC command clears the server cache and restarts logging of the query running time:

DBCC FREEPROCCACHE

Run this query to find the longest running query:

SELECT DISTINCT TOP 10
 t.TEXT QueryName,
 s.execution_count AS ExecutionCount,
 s.max_elapsed_time AS MaxElapsedTime,
 ISNULL(s.total_elapsed_time / s.execution_count, 0) AS AvgElapsedTime,
 s.creation_time AS LogCreatedOn,
 ISNULL(s.execution_count / DATEDIFF(s, s.creation_time, GETDATE()), 0) AS FrequencyPerSec
 FROM sys.dm_exec_query_stats s
 CROSS APPLY sys.dm_exec_sql_text( s.sql_handle ) t
 ORDER BY
 s.max_elapsed_time DESC
 GO 

You should also take a look at the Technet magazine article Optimizing SQL Server Query Performance, which has a query for determining which query is the most expensive read I/O query, as well as guidance on how to look at execution plans and other optimizations.

You can use SQL Profiler to monitor the system in real time to identify slow running statements.