Why should Bolt holes of flanges straddle centrelines of pressure vessels ?  I have noticed them in many standards and fabrication rules.  

Another question is on why Anchor Bolts of Skirts/Pressure vessels straddle centrelines.

A reasoning I got was that straddled holes provided more space for bolt removal than when the bolt-holes were in-line with the centrelines.  Are there any solid reasons for straddling ?

I have always been told that, the bolts holes are positioned off centre, so that if a small leak occurs it will not drip on a bolt!  
If a bolt is at the bottom of the flange it will experience accelerated corrosion, failure and lead to a major leak.

Biggy's answer sounds reasonable but I'm guessing it also has to do with standard convention. If you know the flange you're hooking up to is always going to be two holed then you'll always know how your fitting will be orientated. May not always be necessary, but its a good practice to follow.

I agree with HUSH.  This is a convention that we all are familiar with.  The contractor fabricating adjoining piping can be sure, (unless told otherwise)that his mating flanges must follow that convention in order for the piping to be installed in the right direction.  Similarly, the contractor installing holding-down bolts will be familiar with the convention and will install accordingly.  

In both cases, straddling the centreline can be more accurately varified because a square can be aligned with the two bolt holes or bolts so that the opposite leg is aligned with the vessel or foundation axis.

Regards,
Bill Birch

Something extra I forgot.  For most wessel nozzle (which are horizontal), a spirit level can be used across straddling bolt holts to verify "plumb".

Another point is the configuration of ancilliary items attached to the vessel. For many vessels that are circular is hard to determine the centre line but, when ancilliary items such as support/mounting brackets are attached they are deemed to sit equally across the centre line.

This then means that the reactions from any moments are spread equally through all the bolts without any of them acting as a fulcrum to the bending moment.