Is there something special, unique I can do for the groom either at the church or at the reception... a speech or something? Do people do things like that..

Yes, it is very nice of you to do a reading of some special poem, verse, scripture or something you have written yourself that expresses your feelings for him. A good time to do this at the ceremony is before the vows and after the exchange of rings (check with the officiant for time suggestions and run the reading past him/her before you give it). Keep it short (no more than a few minutes).

You could also do it at the reception, as part of the toast process (best man proposed toast, etc.)