The schema you show, denormalized with all tags for each video stuffed into the Tags string, is badly designed for your purposes -- there is no reasonable way in TSQL to compute a meaningful "commonality" between two strings in such format, and therefore no reasonable way to check what pairs of items have relatively high commonality and thus may be deemed "related". If the schema is untouchable, you'll have to implement a user-defined function (in C# or other .NET language) for the purpose, and even then you will more or less have to scan the whole table since there's no reasonable way to index on such a basis.
If you can redesign the schema (with two more tables: one to hold the tags, and one to give the many-many relationship between tags and videos) there may be better prospects; in this case, some indication on roughly how many (order of magnitude) videos you expect to hav, how many (ditto) distinct tags overall, and roughly what number of tags a video would be expected to have, might allow designing and effective way to pursue your purposes.
Edit: per comments, apparently the schema can be redesigned, although still no indication was given about the numbers I asked, so appropriate indices &c will remain a total mystery. Anyway, suppose the schema is something like (each table can have other columns as desired, just add them to the query; and the VARCHAR lenghts don't matter either):
CREATE TABLE Videos (VideoID INT PRIMARY KEY,
VideoTitle VARCHAR(80));
CREATE TABLE Tags (TagID INT PRIMARY KEY,
TagText VARCHAR(20));
CREATE TABLE VideosTags (VideoID FOREIGN KEY REFERENCES Videos,
TagID FOREIGN KEY REFERENCES Tags,
PRIMARY KEY (VideoId, TagId));
i.e. just the classic 'many-many relationship' textbook example.
Now given the title of a video, say @MyTitle, titles of the 5 videos most "related" to it could easily be queried by, for example:
WITH MyTags(TagId) AS
(
SELECT VT1.TagID
FROM Videos V1
JOIN VideosTags VT1 ON (V1.VideoID=VT1.VideoID)
WHERE V1.VideoTitle=@MyTitle
)
SELECT TOP(5) V2.VideoTitle, COUNT(*) AS CommonTags
FROM Videos V2
JOIN VideosTags VT2 ON (V2.VideoID=VT2.VideoID)
JOIN MyTags ON (VT2.TagId=MyTags.TagId)
GROUP BY V2.VideoId
ORDER BY CommonTags DESC;