tracking health for multiple units of the same type

Actually, you could go with damage counters any way.
Make these damage counters just as big as the unit card size. This helps in handling them. And simply place them below the unit. Now you have a little stack of at least 2 cards when the unit is damaged. The unit itself and the damage counters.
Also, a colour on the side might give away the amount of damage that this unit has taken. If your units only have 4 to 9 health. Counters of 1 and 5 will do. You could use the colours Red and Black.

If you have multiple units on one square, you still can stack them this way. However, the tower might get to big. For preventing that you could also use miniature "whiteboard" cards. Simply write down the damage. And wipe it out if it has to be changed. The con is that you can't get a fast grasp of the situation of the unit.

Do the units use a facing? Or doesn't it matter where they are looking? In that case. You could simply turn them around. Each side of the card (the 4 sides I mean) Have the counters 0, 1, 2 and 3. Then flip over the card for 4, 5, 6 and 7 damage. With 8, the unit is dead and removed any way.
Although, 9 or higher for health would be impossible with this.

Last, perhaps having round units and the numbers simply displayed on a second round piece. All you need now is to turn the second round piece until you have the desired number of health. You even could use 2 rings for health like this.
http://i.ytimg.com/vi/K2_sy57YqSs/maxresdefault.jpg
Observe this picture closely to what I mean.

I hope this helps.

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If it is just a hobby game. I advice to put effort into making the pieces. And I would love to hear more about it.

If you are going to use stand up figures. (which I find awesome) Make the counter as big as half the basis.
With that I mean that you simply lay down the counter ON the basis, visible for all to see. If you need a second counter, you can place this one on the other side of your figure.

I advice not to use 9 different colours. Just 2 or 3.
Reason 1: Colour blind people. You can find on the internet which colours do great together for all people.
Reason 2: This might create confusion. Unless you have numbers printed on them.

If you have 9 as a maximum health. You can use the counters 1 and 3.
1, 1+1, 3, 1+3, 1+1+3, 3+3, 1+3+3, 1+1+3+3, and dead.
Instead of halves; quarters will do even better.

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With this said. Using hiders instead of counters might also work.
The unit already has the numbers printed on the basis. And if the health is reduced, you simply hide the health.
But modding an individual unit will not be possible any more.

May not hurt to do 1, 3, and 5 tokens. This means that you'll never have more than 2 tokens next to a unit unless it has 7 damage (5+1+1 or 3+3+1) which keeps the game less cluttered.

This is elegant, but would probably require a section in the rulebook to explain for players who don't intuit it quickly. :D

Well, you got a point Zag. But I think that he is getting rid of every damaged unit in the game. I mean, that there are 25 units. But only 2 to 3 will be having the damage. Players tend to finish the injured since this is in most cases the best tactical approach.

Perhaps we should await his answer. And maybe you can tell us more.