So this was easier than I expected.  After implementing a rather simple query to take care of this, I instantly had far better performance than I thought I would.  So I'm not sure it's necessary to implement and test the other solutions.
I currently have my database filled with around 200 shaders and 500 tags.  I ran what I think is a somewhat realistic test where I performed 35 different search queries against my stored proc with a varying number of tags, with and without a search term.  I put all of this in a single SQL statement and then I benchmarked the results in ASP.NET.  It consistently ran these 35 searches in under 200 milliseconds.  If I reduced it to just 5 searches then the time goes down to 10 ms.  That kind of performance is awesome.  It helps that my database size is small.  But I think it also helps that the query utilizes indexes well.
One thing I changed in my query was the way I was looking up tags.  I'm now looking up the tags by their id instead of the name.  By doing this I can get away with doing 1 less join, and have the benefit of using an index for the search.  And then I also added "dbo." to the front of the table names after learning that SQL caches queries on a per-user basis.
In case anyone is interested, here's my finished stored proc:
ALTER PROCEDURE [dbo].[search] 
    @search_term    varchar(100) = NULL,
    @tag1           int = NULL,
    @tag2           int = NULL,
    @tag3           int = NULL,
    @tag4           int = NULL,
    @tag5           int = NULL,
    @tag6           int = NULL,
    @tag7           int = NULL,
    @tag8           int = NULL,
    @tag9           int = NULL,
    @tag10          int = NULL
AS
BEGIN
    SET NOCOUNT ON;
    IF LEN(@search_term) > 0
        BEGIN
            SELECT s.shader_id, s.page_name, s.name, s.description, s.download_count, s.rating, s.price FROM dbo.shader s 
            INNER JOIN FREETEXTTABLE(dbo.shader, *, @search_term) AS ft ON s.shader_id = ft.[KEY]
            WHERE (@tag1 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag1))
            AND   (@tag2 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag2))
            AND   (@tag3 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag3))
            AND   (@tag4 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag4))
            AND   (@tag5 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag5))
            AND   (@tag6 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag6))
            AND   (@tag7 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag7))
            AND   (@tag8 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag8))
            AND   (@tag9 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag9))
            AND   (@tag10 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag10))
            ORDER BY ft.[RANK] DESC
        END
    ELSE
        BEGIN
            SELECT s.shader_id, s.page_name, s.name, s.description, s.download_count, s.rating, s.price FROM dbo.shader s 
            WHERE (@tag1 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag1))
            AND   (@tag2 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag2))
            AND   (@tag3 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag3))
            AND   (@tag4 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag4))
            AND   (@tag5 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag5))
            AND   (@tag6 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag6))
            AND   (@tag7 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag7))
            AND   (@tag8 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag8))
            AND   (@tag9 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag9))
            AND   (@tag10 IS NULL OR EXISTS(SELECT 1 AS num FROM dbo.tag_shader_xref tsx WHERE tsx.shader_id = s.shader_id AND tsx.tag_id = @tag10))
        END
END
Even though I didn't exhaust every option, this was still a good exercise because I have proven to myself that my database design is working very well for this task.  And I also learned a lot from posting this question.  I knew exec() was bad because it doesn't cache the query plan.  But I didn't know that sp_executesql caches query plans, and that's very cool.  I also didn't know about Common Table Expressions.  And the link Henrik Opel posted is packed full of good tips for this type of task.  
Of course I still may revisit this a year from now if the database grows drastically.  Until then, thanks everyone for the help.
UPDATE:
So I have a working example of this search engine online at http://www.silverlightxap.com/controls if anyone is interested in seeing this in action.