Insert into clustered index taking too long
Often when I see stuff like this at a client it is from misuse of Database Tuning Advisor. That thing often does REALLY bad things when used by untrained devs/dbas. Tons of overlapping indexes (DTA LOVES covered indexes and does nothing to check for existing indexes that could be just one additional column from covering the currently-analyzed query).
Do beware if/when you go to drop indexes though. Check ALL your code for hard-coded index hints first. Also do not drop unique indexes of any type (unless it is a duplicate of another unique index).