Content Partner, Illuminations, is one-stop shopping for cool interactives for every grade level. I'm sure you will get many replies from members with their favorite interactives for a second grader. But don't miss the occasional resource in Wonderopolis, a site that covers many topics including math, for the younger students.
Wonder of the Day: What Is a Prime Number? - http://www.wonderopolis.org/what-is-a-prime-number/
Wonder of the Day: What is Pi? - http://wonderopolis.org/wonder/what-is-pi/
Wonder of the Day: How Can Math Help You Cook? - http://wonderopolis.org/wonder/get-cooking/
And don't forget to do a search for "Math Games" in Thinkfinity and then click on the Thinkfinity Community Content tab to see resources that members of the community have bookmarked as their favorites. These member-reviewed sites can be very exciting too.
Mangahigh isn't just for High School and now even better it is free. Our school used it last year with our 6th graders and this year I have setup accounts for all of our students. The games are very arcade like which my boys especially enjoy. They also like the fact that other schools can challenge them to competitions. Teachers like it because they can assign students materials based on their skill levels but they play the same games so no on really knows.
One of the games I used to play with my students was "What time is it Mr. Wolf?" This older game was fun for the kids and for me. I would hold a large Judy clock while each of the students had a smaller version in their hand. I would set the students up against the wall and I would stand away from them. They would call out "what time is it Mr. Wolf and I would give them a time. They had to set it on their clock and then hold it up for me to see. Once they had the nod from me they could move the number steps toward me based on the clock. As they got closer and to give more practice one of the responses was "it's time to eat you" during which I would chase the kids back to the wall and start all over. The kids learned time, they got the wiggles out, and they took great pride in becoming the teacher if they crossed past the line directly to my right or left. They never tired of the game. I hope this helps you.
You might want to check out the website of The Kentucky Center for Mathematics, www.kymath.org. Click on Math Tools in the upper right-hand corner, then just explore! Most of the Math Tools are organized by math topic/skill rather than grade level. You can try Games and Puzzles, Resources, Homework Help, Help for Parents, etc. Also, you might want to check out www.funbrain.com where there are 25 different online arcade-style games that can be played at different grade/skill levels.
Kentucky Center for Mathematics
Northern Kentucky University
Have you tried mathwire.com? I use this site quite a bit with my fourth grade math class. There are games and activities for second grade as well. They are some online games listed, but they also have math games you can play during class. We played Feed the Bat the other day and the students loved it.
I really like the wonderopolis site through Thinkfinity. Also, check with the publisher of your math curriculum. I often times use the online games/support that is offered through Math Connects. I would recommend that you really decide on the purpose of using online math games, then make sure that the site offers tools, skills, etc that match your purpose/goal.
I did some tutoring this summer and found a wonderful website called http://www.ixl.com/ It's excellent! It has lots of activities K-12! It's a great place to use as a center activity or at home if you need a child to get that extra practice.
I recently read about Math Chimp that offers 100 free, online, math games that correspond with the elementary common core standards. If you find some you like, please share how your students responded to these resources.
I can attest that PowerMyLearning is a great one. They've got educational games and activities for all subjects and all grades K-12. They even sort the activities by Common Core State Standards, which are becoming increasingly important.
There are a TON of math games and many of them would be perfect for a 2nd grader.
Check out these free interactives from Illuminations geared towards second grade:
For mobile apps, you can use: Deep Sea Duel, Pick-a-Path, Equivalent Fractions, and Math Concentration. Here's a site where you can download them: FREE Apps for your Mobile Devices from Illuminations
Hope this helps!