Thankfully, if you search hard enough, you can find some toddler game sites that have some very cool math games that toddlers will love. Some of these are not overtly about adding or subtracting, but what they do is instill an understanding of counting, organizing and recognizing mathematical patterns through the use of a fun activity toddlers will enjoy.
The following list includes five great toddler game sites that offer useful math games for your child or preschool student.
Kid Space touts itself as a place for "education, fun games and safety for kids online". There are plenty of things for toddlers to do beyond math, but if math games are what you're looking for, this site does have a few offerings.

Kids Space Activities
There are just a few math games available, but they are high quality and very fun to play. One game in particular that is sure to capture the interest of your toddler is the game called "Math Lines".

Math Lines Game
This game follows the general theme of other arcade-style "bubble-shooter" games on the Internet. Most kids learn to play those games very fast, because they're so simple. The entire premise is just matching up colors. However, this game uses numbers instead. The goal is to put numbers together that total to ten.
While many toddlers won't understand the number part of the game at first, by playing for a while, the game will eventually start teaching toddlers how to add two numbers together.
Knowledge Adventure is an online game site like most others out there. The difference is that Knowledge Adventure caters to the younger crowd, and focuses mostly on games that are educational in nature.

Knowledge Adventure Math Games
This site has a nice collection of math games, and surprisingly many of them would be more than appropriate for toddlers. One example is Tower Blocks, a game where the goal is to build the largest tower in the world by dropping blocks from a crane and stacking them up evenly.

Tower Blocks
While this is obviously somewhat arcade in nature, the game actually teaches math concepts in subtle ways. For example, you can only drop 3 blocks, and you'll see dropped blocks count down from three (teaching counting). You will also see the ruler on the left count the number of levels of blocks successfully built.
This kind of game is a great way to introduce counting and addition to young minds.
SoftSchools.com is a large educational site covering topics like phonics, spanish, science, social studies and more. The math content of the site is by far the largest. There is an entire section focused on just preschool math games and worksheets.

Preschool Math Games
This is also one of the few sites that offer games that are very much focused on educational concepts that toddlers need to learn before going to kindergarten. One example of this is the "Counting up to 10" game, which teaches the very simple, yet important, concept of counting objects.

Counting Games
Many parents send their toddlers to sites that assume they already know how to add and subtract basic numbers, but for children that aren't quite at that level of understanding yet, these Soft Schools activities are a very good place to start.
Cookie is a well-made website that really caters to the educational community. The site offers worksheets, arts and crafts, videos and games for the classroom. Under the games section, you'll find a nice variety of cool math games. Those games have the sole purpose of introducing some concept of math to the pre-K or Kindergarten age student.

Lots of Math Games at Cookie.com
Don't let the name of the site fool you - these games aren't just junk food for the young mind. They are the sort of activities that you'd hope to find on the computer in any preschool or Kindergarten classroom.

Number Identification Game
The games focus on tasks as simple as just identifying numbers - one of the very first stages in any young student's math education. No teacher or parent could go wrong having a toddler play the games found at this website.
Simply Named "Kids Math Games Online", this site is all about offering learning games and lots of activities to instill a strong mathematical education in any child.

Kids Math Games Main Page
There are more than just games on this site. You'll find videos, worksheets, "facts", quizzes and more. But if games are what you're looking for, this is the site to visit. These are all interactive, well-made games that focus on math principles, but are still very fun to play. One example is the Kindergarten counting game.

Kindergarten Counting Game
This game will feel like an arcade game to the toddler, but ultimate it teaches counting by showing the student the number they need to catch. All of the numbers are moving around like little insects, and it's up to the student to find the matching number and click on it, or "catch" it. It is a creative and fun way to teach young toddlers how to count.
As you can see, there are plenty of options for math games that will truly teach toddlers, and not just entertain them.
Any of these games or websites would be more than appropriate for a classroom environment, and as an educator, you could also recommend them to parents as a good way for children to practice at home, the math concepts that they've learned in the classroom.