Is my SQL Server patched?
To answer in reverse order

What version am I on?

There are two different queries that I use to identify my SQL Server level.

The first is @@version. The nice thing about this is that it brings back OS level information as well. The challenge with it is that it's a big dump of text and you have to parse that to find the relevant bits. 

e.g.

SELECT @@version;

/*
Microsoft SQL Server 2014 - 12.0.4416.0 (X64) 
    Jun 11 2015 19:18:41 
    Copyright (c) Microsoft Corporation
    Developer Edition (64-bit) on Windows NT 6.3 &lt;X64&gt; (Build 9600: ) (Hypervisor)
*/


My preference is to use ServerProperties as I can individually identify the elements.

SELECT 
    SERVERPROPERTY('productversion') AS ProductVersion
,   SERVERPROPERTY ('productlevel') AS ProductLevel
,   SERVERPROPERTY ('edition') AS Edition;

/*
ProductVersion  ProductLevel    Edition
12.0.4416.0     SP1             Developer Edition (64-bit)
*/


Is there native functionality to check for patches?

Nothing that I'm aware of. If the host OS has Windows Update service running and someone has specified "Include patches for other MS products" then you might get patches installed for SQL Server. 

But, if you're a professional, you're probably not interested in waiting for a patch to be listed in WSUS or you'd like to validate that the patch works for your environment. That's going to involve reading knowledge base (KB) articles and testing. 

How can I tell if my SQL Server instances are patched?

Lacking anything built into the product, I have been referencing sqlserverbuilds.blogspot.com. But there are plenty of other sites out there attempting to offer the same consolidated list of patches, such as:


http://sqlserverupdates.com/
http://blogs.sqlsentry.com/category/sql-server-builds/


I have taken the data from that blog and converted it to a View, dbo.PatchLevel. That view exposes all the patches. This view is truncated to only cover 2016 and 2014, otherwise I blow the character limit for answers.

CREATE VIEW dbo.PatchLevel
AS
-- data from http://sqlserverbuilds.blogspot.com
WITH SRC(Build,[File version],[KB / Description],[Release Date], SimpleVersion) AS
(
    SELECT
        CASE LEN(D.Build) - LEN(REPLACE(D.Build, '.', ''))
            WHEN 3 THEN REPLACE(D.Build, '.00.', '.0.')
            WHEN 2 THEN REPLACE(D.Build, '.00.', '.0.') + '.0'
        END AS Build
    ,   D.FileVersion
    ,   D.KB
    ,   CAST(REPLACE(D.ReleaseDate, ' *new', '') AS date) AS ReleaseDate
    ,   CAST(LEFT(D.Build, 4) AS decimal(4,2))
    FROM
    (
        VALUES
            ('13.00.500.53','2016.130.500.53','Microsoft SQL Server 2016 Community Technology Preview 2.3 (CTP2.3)','August 28, 2015 *new')
        ,   ('13.00.407.1','2016.130.407.1','Microsoft SQL Server 2016 Community Technology Preview 2.2 (CTP2.2)','July 23, 2015')
        ,   ('13.00.400.91','2016.130.400.91','Microsoft SQL Server 2016 Community Technology Preview 2.2 (CTP2.2) [withdrawn]','July 22, 2015')
        ,   ('13.00.300.44','2016.130.300.444','Microsoft SQL Server 2016 Community Technology Preview 2.1 (CTP2.1)','June 24, 2015')
        ,   ('13.00.200.172','2016.130.200.172','Microsoft SQL Server 2016 Community Technology Preview 2 (CTP2)','May 27, 2015')
        ,   ('12.00.4427','2014.120.4427.24','3094221 Cumulative update package 3 (CU3) for SQL Server 2014 Service Pack 1','October 21, 2015 *new')
        ,   ('12.00.4422','2014.120.4422.0','3075950 Cumulative update package 2 (CU2) for SQL Server 2014 Service Pack 1','August 17, 2015')
        ,   ('12.00.4416','2014.120.4416.0','3067839 Cumulative update package 1 (CU1) for SQL Server 2014 Service Pack 1','June 22, 2015')
        ,   ('12.00.4213','2014.120.4213.0','MS15-058: Description of the nonsecurity update for SQL Server 2014 Service Pack 1 GDR: July 14, 2015','July 14, 2015')
        ,   ('12.00.4100','2014.120.4100.1','SQL Server 2014 Service Pack 1 (SP1)','May 14, 2015')
        ,   ('12.00.4050','2014.120.4050.0','SQL Server 2014 Service Pack 1 (SP1) [withdrawn]','April 15, 2015')
        ,   ('12.00.2556','2014.120.2556.4','3094220 Cumulative update package 10 (CU10) for SQL Server 2014','October 20, 2015 *new')
        ,   ('12.00.2553','2014.120.2553.0','3075949 Cumulative update package 9 (CU9) for SQL Server 2014','August 17, 2015')
        ,   ('12.00.2548','2014.120.2548.0','MS15-058: Description of the security update for SQL Server 2014 QFE: July 14, 2015','July 14, 2015')
        ,   ('12.00.2546','2014.120.2546.0','3067836 Cumulative update package 8 (CU8) for SQL Server 2014','June 22, 2015')
        ,   ('12.00.2506','2014.120.2506.0','3063054 Update enables Premium Storage support for Data files on Azure Storage and resolves backup failures','May 19, 2015')
        ,   ('12.00.2505','2014.120.2505.0','3052167 FIX: Error 1205 when you execute parallel query that contains outer join operators in SQL Server 2014','May 19, 2015')
        ,   ('12.00.2504','2014.120.2504.0','2999809 FIX: Poor performance when a query contains table joins in SQL Server 2014','May 5, 2015')
        ,   ('12.00.2504','2014.120.2504.0','3058512 FIX: Unpivot Transformation task changes null to zero or empty strings in SSIS 2014','May 5, 2015')
        ,   ('12.00.2495','2014.120.2495.0','3046038 Cumulative update package 7 (CU7) for SQL Server 2014','April 23, 2015')
        ,   ('12.00.2488','2014.120.2488.0','3048751 FIX: Deadlock cannot be resolved automatically when you run a SELECT query that can result in a parallel batch-mode scan','April 1, 2015')
        ,   ('12.00.2485','2014.120.2485.0','3043788 An on-demand hotfix update package is available for SQL Server 2014','March 16, 2015')
        ,   ('12.00.2480','2014.120.2480.0','3031047 Cumulative update package 6 (CU6) for SQL Server 2014','February 16, 2015')
        ,   ('12.00.2474','2014.120.2474.0','3034679 FIX: AlwaysOn availability groups are reported as NOT SYNCHRONIZING','May 15, 2015')
        ,   ('12.00.2472','2014.120.2472.0','3032087 FIX: Cannot show requested dialog after you connect to the latest SQL Database Update V12 (preview) with SQL Server 2014','January 28, 2015')
        ,   ('12.00.2464','2014.120.2464.0','3024815 Large query compilation waits on RESOURCE_SEMAPHORE_QUERY_COMPILE in SQL Server 2014','January 5, 2015')
        ,   ('12.00.2456','2014.120.2456.0','3011055 Cumulative update package 5 (CU5) for SQL Server 2014','December 18, 2014')
        ,   ('12.00.2436','2014.120.2436.0','3014867 FIX: "Remote hardening failure" exception cannot be caught and a potential data loss when you use SQL Server 2014','November 27, 2014')
        ,   ('12.00.2430','2014.120.2430.0','2999197 Cumulative update package 4 (CU4) for SQL Server 2014','October 21, 2014')
        ,   ('12.00.2423','2014.120.2423.0','3007050 FIX: RTDATA_LIST waits when you run natively stored procedures that encounter expected failures in SQL Server 2014','October 22, 2014')
        ,   ('12.00.2405','2014.120.2405.0','2999809 FIX: Poor performance when a query contains table joins in SQL Server 2014','September 25, 2014')
        ,   ('12.00.2402','2014.120.2402.0','2984923 Cumulative update package 3 (CU3) for SQL Server 2014','August 18, 2014')
        ,   ('12.00.2381','2014.120.2381.0','2977316 MS14-044: Description of the security update for SQL Server 2014 (QFE)','August 12, 2014')
        ,   ('12.00.2370','2014.120.2370.0','2967546 Cumulative update package 2 (CU2) for SQL Server 2014','June 27, 2014')
        ,   ('12.00.2342','2014.120.2342.0','2931693 Cumulative update package 1 (CU1) for SQL Server 2014','April 21, 2014')
        ,   ('12.00.2269','2014.120.2269.0','3045324 MS15-058: Description of the security update for SQL Server 2014 GDR: July 14, 2015','July 14, 2015')
        ,   ('12.00.2254','2014.120.2254.0','2977315 MS14-044: Description of the security update for SQL Server 2014 (GDR)','August 12, 2014')
        ,   ('12.00.2000','2014.120.2000.8','SQL Server 2014 RTM','April 1, 2014')
        ,   ('12.00.1524','2014.120.1524.0','Microsoft SQL Server 2014 Community Technology Preview 2 (CTP2)','October 15, 2013')
    ) D(Build,FileVersion,KB,ReleaseDate)
)
SELECT
    SRC.Build
,   SRC.[File version]
,   SRC.[KB / Description]
,   SRC.[Release Date]
,   SRC.SimpleVersion
FROM
    SRC;
GO


I have a second view, yes nested view - bad me, dbo.MyPatchLevel which uses the version data from above to compare to my current instance and generate output to let me know just how bad it is.

CREATE VIEW dbo.MyPatchLevel
AS
WITH MostRecentBuild AS
(
    SELECT
        SRC.Build
    ,   SRC.[Release Date]
    ,   SRC.SimpleVersion
    ,   SRC.[KB / Description]
    FROM
        dbo.PatchLevel AS SRC
    WHERE
        SRC.[Release Date] =
    (
        SELECT
            MAX(SRCI.[Release Date])
        FROM
            dbo.PatchLevel AS SRCI
        WHERE
            SRCI.SimpleVersion = SRC.SimpleVersion
    )
    AND
        SRC.Build =
    (
        SELECT
            MAX(SRCI.Build)
        FROM
            dbo.PatchLevel AS SRCI
        WHERE
            SRCI.SimpleVersion = SRC.SimpleVersion
            AND SRCI.[Release Date] = SRC.[Release Date]
    )

)
, MyVersion AS
(
    SELECT
        SRC.Build
    ,   SRC.[File version]
    ,   MRB.[KB / Description]
    ,   SRC.[Release Date]
    ,   D.ProductVersion
    ,   D.ProductLevel
    ,   D.Edition
    ,   D.Version
    ,   SRC.SimpleVersion
    ,   MRB.Build AS MostRecentBuild
    ,   MRB.[Release Date] AS MostRecentReleaseDate
    FROM
        dbo.PatchLevel AS SRC
        INNER JOIN
        (
            SELECT 
                SERVERPROPERTY('productversion') AS ProductVersion
            ,   SERVERPROPERTY ('productlevel') AS ProductLevel
            ,   SERVERPROPERTY ('edition') AS Edition
            ,   @@VERSION AS Version
        )D 
        ON D.ProductVersion  = SRC.Build
        INNER JOIN
            MostRecentBuild AS MRB
            ON MRB.SimpleVersion = SRC.SimpleVersion
)
SELECT
    MV.ProductVersion AS CurrentVersion
,   MV.MostRecentBuild
,   MV.[Release Date]
,   MV.MostRecentReleaseDate
,   DATEDIFF(DAY, MV.[Release Date], MV.MostRecentReleaseDate) AS DaysSincePatchAvailable
,   MV.[File version]
,   MV.ProductLevel
,   MV.[KB / Description] AS [Most Recent KB / Description]
,   MV.Edition
,   MV.Version
,   MV.SimpleVersion
,   CAST(SERVERPROPERTY('ComputerNamePhysicalNetBIOS') AS sysname) AS Server
,   CAST(SERVERPROPERTY('InstanceName') AS sysname) AS Instance
,   CAST(SERVERPROPERTY('ServerName') AS sysname)  AS ServerName
FROM
    MyVersion AS MV;
GO


I'd use a query like

SELECT
    MPL.CurrentVersion
,   MPL.MostRecentBuild
,   MPL.[Release Date]
,   MPL.MostRecentReleaseDate
,   MPL.DaysSincePatchAvailable
,   MPL.[Most Recent KB / Description]
FROM
    dbo.MyPatchLevel AS MPL;


Results

CurrentVersion  MostRecentBuild  Release Date  MostRecentReleaseDate  DaysSincePatchAvailable  Most Recent KB / Description
12.0.4416.0     12.0.4422.0      2015-06-22    2015-08-17             56                       3075950 Cumulative update package 2 (CU2) for SQL Server 2014 Service Pack 1


Armed with these query results, I know whether I'm patched up to date, how long it's been since I've patched and what the KB is to go read up on the current patch state.

Scripts are also hosted on github