As I'm in the process of a major home theatre renovation, I have been trying to figure out if I should angle-in my M60's toward the centre of the room. The room is 13.5 feet wide and 19.5 feet long. If the M60's are near the outer walls, does having them angled-in add anything?

It really depends on the room, where you sit, and what you like.

We sit about 11 feet from the front wall. I used to have the M60's angled-in but just before I ripped the room apart I straightened them out and noticed no difference. One friend said I simply must angle them in, but every online guide to speaker placement always shows the mains straight on.

Bayne, the idea is that generally speakers sound best on-axis, so they should be slightly toed-in so that the tweeters point at your ears. In some cases, if the treble is too prominent on-axis, having them pointed straight ahead may be more satisfactory.

Toeing them in creates a sweet spot where the sound from each speaker intersects, well sometimes slightly in front of this point or behind depending on the room, your personal tastes etc.

The M60's have excellent off axis response so not having them toed in shouldn't be a big deal nor necessary, especially if you have tried it and noticed no difference.

It depends, you need to test different angles and used what sounds best. The front of my theater room is about 15ft wide, and I have my 80's toed in just a little bit. For me, to much toe in affected the sound for the people sitting off to the sides and those respective speakers.

Try them in various positions, straight, toed in, slightly toed in ect....leave them where you feel they sound best. It doesn't cost you anything to move the speakers around a little.

With that great a length to the room, could you sit back a bit farther from the speakers?

In doing some blind listening, i've often setup the 'stage' such that the listening location was far enough back from the two test speakers that you could not discern a left or right cue when switching between them. The soundstage is presented clear in front of the listening position.
This does of course make things a bit more difficult to setup a surround sound field as the side and rear surrounds become that much more important the further back one sits from the mains and centre channel.

Point being, you would not need any toeing in of a speaker in this configuration.