There should be an option to choose between two ways for the connector line to connect to the shape - one is like it works for example in Powerpoint (to the edge of the shape, with different position options), and the other way should be to the center of the shape, but not visible inside the the shape. This allows the shape to be moved around without needing to change connector position.

A related request now exists about Callout Tool, similar to one Acrobat has:
http://illustrator.uservoice.com/forums/333657/suggestions/48286484

Yes, please

Indeed, either InDesign or illustrator need this.

Line that connects two shapes at centroid or a user set connection point.
Line stretches and remains linked if objects are moved. Ability to constrain such lock angle or length. Connecting line can be made curved, straight, freehand or angled as in a flow chart. Can apply color, gradient, thickness, fill, shadow as with any shape. More than one line can spawn from same spot to another shape.

good, a very needed feature

When they do, it has to have an option to connect to the center of an object so object kan be moved around without having to change the connector point.

VERY GOOD IDEA!!!

VERY GOOD IDEA!!!

VERY NEEDED!

This is a good idea adobe. It's already possible in AE. Would be useful in indesign as well.

I would like a visio type tool for not just flowcharting, but for other layout type obects like visio.

Most of my prototyping for sequential screens, websites, interface designs and animations are done in illustrator. Virtually every project I work on uses a flow chart for working out the logics. By being able to do this in illustrator will be the best thing ever as can clearly map up flow of logical thinking. This will add so much productivity for all designers across the planet as part of their work flow. A feature that will be as useful as illustrator itself. Mike

Would be awesome! Mirra/Realtime board does this exceptionally well and has become my go to for it. But native in AI would be so much better.

This is a quite needed feature
I always search this so I can create mind maps and also very good designs that explain things.
In the ideal, we should be able to create a point group. This will allow to have one or more points grouped to one object and others to another object. It's as simple as that... to have the ability to create avertex groups

I would suggest that these connectors should be a special kind of line with a separate tool. Just to make sure I still have the option to draw "normal" lines as before, and (maybe in a future version) can use "connected" lines if I need them.

I'm really surprised that this isn't a feature yet.