Abandoned Shrine:
Go for it, +2 dex, no penalty. Creepy Shrine: Go for it, +2 str, no penalty.

Cryptic:
Full mana ball, useful. If you're surrounded in a corridor and you have telekinesis, you can also wipe out a ton of enemies that way from the Nova.

Divine:
Gives you free potions, use it :)

Eerie:
Despite the message, it's +2 to Magic with no penalities.

Eldritch:
Before using it, go to town and buy as many regular/full healing potions as you can. Then use the shrine. They'll all become Rejuvenation potions. If you don't want to use them, you can sell them for 70 gold profit on the regular, and 100 (I think) gold profit on the fulls.

Enchanted:
Unless you've only got one or two spells, use it. It's easy to recover one spell level for one particular spell, it's hard to gain a level for 10+ spells. Very nice for Sorcerers and Rogues.

Fascinating Shrine:
Avoid like the Plague. The +2 spell level isn't worth the permanent Mana loss.

Glimmering Shrine:
Use, but beforehand, have everyone in your party give all their unidentified equipment to you.

Gloomy:
Have everyone give you their armor, but drop all weapons before use.

Hidden:
Unless you've got very low durability equipment you don't want to accidentally weaken, use it. Also, if you want to make a specific item stronger, drop everything but that item and a generic item found on the floor. 50/50 chance you'll get lucky (very useful with a Thinking Cap).

Holy:
Your choice, it really doesn't matter (it's only like casting phasing).

Magical:
If you're a warrior or a rogue with low magic, it may not be worth it. If you're a high level Rogue or Sorcerer, go for it.

Mysterious:
It's your choice. Personally, I avoid all the shrines that lower stats, even if they do raise one or more.

Ornate:
Avoid. Holy Bolt's easy enough to raise levels, but the mana loss is permanent.

Quiet:
Unless someone else in your party needs it badly, use it. +2 to vitality, no penalities.

Religious:
Before using it, have everyone give you their weapons to repair.

Sacred:
Avoid as well, as the spell levels aren't worth the mana loss.

Secluded:
Sure, a full map's always worth having (even if you can't tell where you haven't been yet anymore).

Spiritual:
If you're low on money, empty your pockets before using. If you're rich enough, you can just ignore it (it's usually only around 700 gold).

Spooky:
If you can, have someone else use the shrine so you get potions ;) Always worth using.

Stone:
Useless unless you have staves. If more than one person has them, empty the staff before using, and give all of them to one person, who uses the shrine.

Tainted:
From my experience, people hate it when their stats change without their prior approval, and this shrine'll do that. Ask before using (I usually avoid using it).

Weird:
Have everyone give the user of the shrine their weapons before using it.

Blood Fountain/Purifying Spring:
Sure, use it all you want. It's unlimited use, free Health/Mana recovery.

Fountain of Tears:
It's your choice, but I always avoid the shrines/objects that lower my stats and raise others.

Goat Shrine/Cauldron:
Once again, personal choice. I think it's too risky, although 9 out of 10 times I use a Goat Shrine, I got Mana Shield. Choose for yourself.