While a lot of the attention with the new 40K psychic phase has been focused on generating as many dice and daemons as possible, the new phase inherently brings about some important changes that I haven't seen discussed yet (it may have been, I just haven't seen it).
The fact that psychic powers all happen in one phase - and where it is placed in the turn sequence - has important effects that you should be aware of, even when you don't bring psykers of your own.
There's been some talk of how this affects blessings - you have to think ahead with them, even with your force weapons. Think you might be attacked by the enemy monstrous creature next turn? Go ahead and get that force weapon ready now so it will be warmed up in time.
Psychic powers being their own phase also opens up some opportunities for powers that are often overlooked in favor of more "useful" abilities - the oft-maligned witchfire powers. Previously these were just a different kind of shooting weapon, tied in with the rest of a unit's shooting. Now a psyker in a unit basically gets split fire for free, being able to blast one unit with witchfire and his unit can later shoot something else, allowing you to have the protection of the unit without losing the flexibility of independent action. Now in a separate phase, witchfires can also let you cause more morale tests than ever - psychically blast the enemy and cause a test, then if he's still around you can cause another check with your regular shooting.
Depending on the powers involved, you can also use the separate phase as a defensive bonus. In sixth edition, you could be sitting in your transport, get melta'd out of it and immediately hit with Destructor, Psychic Shriek, etc. Now, if your enemy can't crack your rides open in the psychic phase itself, he can't use those nasty anti-infantry powers on you. If he has to wait for his shooting to destroy your transports, you have another turn to deal with him before he can start Shrieking you. Pay attention to what powers your opponent has available and plan accordingly.
So, just some thoughts to spur your own - there's a whole lot out there beyond summoning daemons and Invisibility!