People who reply with good ideas, I'll edit this post to include them

UI

Shop Info:  Couldn't the data be listed right by the icon without having the hover over it?  It's not like there are 500 items..
Shop Color Coding: Commonly used bonuses should have an associated color(IE: +armor in green, +health in red, +mana in blue, +attack speed in purple, +damage in orange or whatever.  It would make browsing and comparing easier for new players I think.)
Rearranging/resizing: There should be something in options that brings up the ui elements hwere it allows you to drag them around and increase/decrease their size.  Then when ally portraits are added (if theyare, i guess) we can move where they are, make them horizontal or verticle, move debuff icons, so on.
SHOP BLACKSMITH UPGRADES:  http://forums.demigodthegame.com/323546 needed its own thread.

(ADDED 8:13 PM sept06)
Chat "beep": Need it when someone says a message.  Also, text needs to scale with resolution.  And the chat beep needs to only trigger the first time someone sends a message every 10 seconds(so spamming doesn't spam beeps.
-Their first message would make the beep, and then additional messages wouldn't until 10 seconds later.  Maybe 5, i don't know.  Chatbeep when people spam is annoying, but not knowing people have said anything is annoying too. (ADDED 1:48 AM sept05)
Health bars: Holding alt or something should show everythings health bars.  People with low health should have their bars automatically show(maybe start fading in at 30%, being solid at 20%).  The health bars ideally should offset so they don't overlap, and you could click the healthbars to attack. (ADDED 2:44 AM sept05) The tilde settings need to be saved.. i keep ahving to cycle at the start of every match. (ADDED 3:59 PM april25)
Target Highlight: Whoever you're targeting with a DD spell (if engine permits.. aoe spells too would be nice to see who they'll hit like in wc3..) should have like a white outline or glow around them, or something. (ADDED 3:56 AM sept05)
-This one has been partially added.. It works for single targetting, but not aoe's.
Teamate status: On the bottom left, beside your center bar (starting near the middle[as close to without overlapping the current ui there, of course] then going towards the left[not from the left corner inwards.  The more teamates, the more number of icons going left].  Clicking on them should select that teamate(selection detailed below in controls).  It should show Demigod portrait, health, there should also be "Attacking: ... minotaur/player name/archer/healer/giant/angel/etc with an arrow, clicking the words or arrow would select the same target as your teamate. (ADDED 3:56 AM sept05)
DoT damage numbers: The numbers should add together.  IE when UB uses his DoT the number should stay there going from 40, to 80, to 120, to 160, and so on, not show 40 over and over. (ADDED 9:26 PM March17)
Mana until castable: There should be a timer like the cooldown timer showing how long it'll be until you'll naturally regen enough mana to use a skill that is "blued-out". (ADDED 10:04 PM sept07)
Debuff/Buff timers: Overtop of or above debuff/buff icons it should have a timer showing when it'll end. (ADDED 9:17 PM april26)

Controls

Select target:  Right click is attack, obviously.  But left click should select buildings, units, other Demigods.  This should bring up their portrait, a bigger spell bar positioned above your own(smaller of course). Left clicking the ground would clear your selection.
Attack selected target:  Then hit space.(Camera rotate can be moved.. dont need it on space)   In this way you can keep something selected like say, an enemy Demigod.  You can right click on enemy creeps to kill them, and then when you want to attack the Demigod(say, they came in range) you hit space and there is no miss-clicking. Would be used on towers, stronghold, ALLIES TOO.
Use spell on selected target:  Simply hitting the hotkey for a single-target skills with something/someone selected would use the skill on them.(with nothing selected the normal target selection currently in use would be used).  direct-target as in mines, aoe attacks, rooks hammer slam(seeing as how it targets the ground) wouldn't apply and would be targetting how they are now.  Snipe is an example of what would be used on what you have selected.
Or say for Sedna. You can keep a nearby ally selected to heal them very quickly, while you right click to attack people
Queuing:  Shift+click should cue skill orders, and pretty much anything that you could queue.  (ADDED 5:10 PM sept05)
ESC to close menus:  Pressing ESC should close menus(shops, skills, ETC).  Only bringing up the esc menu when you have no menus open.  This one annoys me sooo much.  I keep hitting esc to close the shop and skills screen. (ADDED 2:09 PM sept08)
Rearrange skill hotkeys:  Should be able to drag the skills into the order you want and the game remember that order. (ADDED 2:59 AM sept09)

Ally portrait targetting:   You should be able to click on your own characters portrait, or an allies, to use a skill on them more easily. (ADDED 3:59 PM april25)
INTERRUPTED! float text instead of STUNNED! on interrupts:  This really should of be added a long time ago after it was shown how good interupts work for the gameplay.   (ADDED 3:51 PM may01)

Misc

Shopping while dead:  We should be able to view the list of items at the shop while dead and purchase when we rez. (ADDED 3:16 AM sept05)
Speccing while dead:  ^ Same thing. (ADDED 3:16 AM sept05)
Pinging: Ctrl+clicking onthe ground should make a ping for allies.  It should have some piller of light kind of effect or something.  Right now all this does is ping the minimap.  It should make an effect on the ground like god rays and "move here" text!
-People who's screens can't see it should have an arrow on their screen pointing to it.
-When your health is low the healing crystal should be pinged which only you can view. (new players sometimes haven't figured out they can heal there.) (ADDED 5:28 PM sept05)
Range:  MEASURE IN METERS!  Still here because AoE sizes aren't listed (edited 3:59 PM april25)
- This has partially been added.  Ranges show this, but aoe's are still a mystery.

ADDED 2:44AM sept09:

Just a photoshop mockup.. not really how i think it should actually look except for the death messages and chat, but it puts the point across.

Things that need clearifying:

1. The xp/gold log would show something like "00:01-05:00 ... Killing ## minotaurs and gained 3342 gold, 500 xp" or whatever.  5 minute increments, with the newest one showing real-time.
2. self explainitory.
3. self explainitory
4. Hover over names in kill messages or chat to show what they have equiped.  Hover over the items for details on them.  Same for portrait when you have them selected.
5. Similar to seeing equip.. hover over the skill someone used to see details on it.
   I think Tyo said they're going to make items and/or levels effect skills, which is good.. so this should show what the skill actually does based on their character.
   Stats modified by character in yellow for intuitiveness.
6. Kills/Deaths messages like an FPS.  This is currently up top and i never notice them.  Mid-bottom right is better, please!
7. self explainitory.
8. LEFT CLICK TO SELECT AND YOU SEE THIS!.  Need left click to select like i said above! ;[  For like healers it'd say how they heal for 10%.  If you selected a potion it'd say it heals, a blue scroll it'd say it gives mana, fortress it'd say it shoots rocks at stuff, so on!
   
   Right now left click does nothing that right click doesn't also do.
   I'm not suggesting to remove left clicking to attack, please no one get confused.  I like right click to attack also.  I like both, depends on the situation.
   So right click for instant-action.  Left click and space to select and confirm action.
9. Teamate status like i suggested before earlier in the post.  For smaller resolutions this would have to be along the side..  I use 1600x1200 myself and want them on the bottom like this.
   Clicking portrait should select the teamate.  (good for spells that target allies!)  Right clicking or double clicking center your camera on them.
   
10. Something showing who your teamate is attacking.  Clicking on any part of it would select the same target they are attacking so you can coordinate!

Have been added:

Remappable keys:  I assume this is a given, but just in case not, i'll throw it in here.  (ADDED 5:10 PM sept05)
Skills:  1-2-3-4 for skills..  Why are these for control groups like an RTS when you'll only control your one hero?  In the Assassins case you can't select anything else to control(which is GREAT!! Omg it frustrates me so much in DotA how i accidently click off my hero!)
Crits numbers: The crits should be adjusted some so that when you get a critical hit it says "Critical Hit - #!" instead of just "Critical Hit!" over your Demigod.  It's easier to see then than with seeing the crit over your demigod while the damage number is over what you hit.  (ADDED 9:26 PM sept05)
Minimap: Something very very light weight.  Like a translucent outline of the map that shows just the Demigods.
Shop Tabs:  Couldn't we just have one shop with tabs for each set of items?  (I heard this is coming, wasn't sure)
Life Leach numbers: When you leach life you should get a red +# over your head, like the green +# you get from being healed. (ADDED 9:26 PM sept05)