Psi Healing: Like medkit, but can be done ranged. Upgraded skill may become AoE effect instead of doing higher heals.
Psychic Surgery: A slow, costy ability that restores "unhealable" hp.
Empathy: See enemy hp and/or role, if originally hidden.
Scrying: A sensor probe not limited by walls.
Clairvoyant: See further and/or wider.
Precognition: See enemy plan. The plan may change with player action. Cue Invisible Inc.
Retrocognition: Like motion tracker.
Daze: Reduce or Eliminate target overwatch.
Mind Trick: Make a unit immune to enemy overwatch.
Psi cloak / distorion: Reduce accuracy of non-mechanic enemies agaist a target or area.
Mind Shade: Same as above but used on enemy.
Pyrokinetic: Remotely start fire, put out fire, or ignite grenade.
Apportation / Psychokinesis Hand: Open/Close/Pickup/Move/Drop remotely. An ability to move a missed grenade would be nice, if they explode at end of turn like X1.
Psychokinesis Shield: Project an energy field that reduce damage (think mass effect)
Psychokinesis Push/Pull: Moving alies sounds like fun.
Note: If these sounds like magic, there is a good reason. They are easier to balance than panic and mind control.