I have started a new game with a party containing a Priest, and have been having her pray a lot. Here are some of the effects I noticed:
Prayer goes unheard (likely the equivalent of a fizzle)
Bless
Heal Wounds (on injured character)
Rest All
Guardian Angel

This is just what I have seen so far this playthrough.

By the way, having a Priest with high Piety can be helpful early on: I have Armorplate Power 3 active and I haven't even left the lower monastery!

Edit: Just saw Magic Missiles (though there was only one target at the time it was used).
Edit 2: Just saw the message "think of it as a learning experience" (no obvious effect)
Edit 3: "Pennies from heaven!" (Party gets 100 gold.)
Edit 4: Heal All (see latest post), Bless can go up to power 8

Never used a priest. Bishops are just so much better.

In terms of power they probably are. Doesn't make the Priest bad. I'd say Priests are pretty good actually. In specific parties you might even argue that they're better. Also it doesn't make the Bishop necessarily more enjoyable. After all the Bishop's power relies heavily on grinding his skills, which isn't needed for a Priest. On top of that the thing I like most about Wizardry is it's long term fun, which for me relies heavily on presenting lots of opportunities for self-restricted challenges - reason enough to not just consider raw power the be-all-end-all criteria for a good character.

In any case I'll follow this thread since I have no clue what a miracle can do.
Thanks for sharing dtgreene!

Actually, Priests have some advantages over Bishops.

1. Lower stat requirements. This allows a Dwarf Priest to get Power Strike at level 11. A Bishop wouldn't be able to get Power Strike as quickly. This is actually faster than most hybrids. (One trick is to create a Priest and then change her to a Lord or Valkyrie to get Power Strike on a hybrid sooner.)
2. More HP. This means that a Priest is more able to survive if put in the front ranks. (I suggest giving her a mace and a shield if you do this.)
3. Can more easily learn spells, especially early in the game. Getting Armorplate while still in the Monastery if feasible for a Priest, and with high Piety, using it at Power 3 might be possible by Arnika Road.

One way to look at Priests is to think of them as hybrids, except balanced a little differently. Hybrids like Lord/Valkyrie are basically fighters first and spellcasters second; Priests are the other way around, but can still function as fighters. A Priest with 100+ Strength, Power Strike, and a good weapon (Staff of Doom/Flame Staff/Diamond Eyes/The Mauler) can actually be a rather effective physical attacker. I actually happen to enjoy this aspect of the Bishop.

That's really strange. Not that I would make a difference for Bless (PL only affects duration).