2D games are making a big come back with the proliferation of mobile games, HTML5 and major support of big publishers. Producing them now have been much easier than before with tools like Unity and help of online 2D Game Asset stores. Below is a list of top 10 2D games asset stores you can find online, not ranked in any order. Some commercial and some free.
** Not ranked in any order **
1. Unity Asset Store (commercial)
Biggest commercial game assets site. No you don't have to use the Unity engine to use games assets offered on the Unity asset store, you can simply download a free copy of Unity and download assets through the Unity asset store online. Game assets will be imported into Unity, and the files will be saved into your Unity project folder. You can use the saved game assets in any 2D game engine. Many people may not know Unity is a very successful 2D game engine, in the hands of professional game developers. Amazing variety of highly successful 2D games have been created such as Rovio's smash hit, Bad Piggies. The integrated asset store offers a large range of 2D assets designed to make well use of Unity's 2D physics engine.
https://www.assetstore.unity3d.com/
2. GameDev Market (commercial)
GameDev Market is quite a new entry, like Super Game Asset it is very well organised into different categories. The offer both 2D and 3D including Game UI, character sprites, icons and environments. It is a market so all assets are artist submissions and it is growing very quickly.
https://www.gamedevmarket.net/
3. Graphicriver - Game Assets (commercial)
Graphicriver is the world's most popular stock image resource, with the proliferation of casual games on mobile they have recently started a specific category just for game assets, and it is all 2D. This is a trustable source for quality game resources as all assets will be reviewed by envato internally before getting listed on the site. Plus you have community review on the sources as well. It is a constantly-growing source with great support from envato.
http://graphicriver.net/category/game-assets
4. Scirra Store (commercial)
Scirra is the developer of Construct 2, a popular HTML5 2D game editor and they now have their own game asset store. You don't have to use them in Construct 2 it is perfectly okay to use in any 2D editor really. The game assets are categorized in graphics, sound, music and even game templates which can help you start a new game quickly in Construct 2.
5. Game Art Partners (commercial)
Plenty for 2D platform games. This site has plenty of 2D game assets for you. All assets are very cartoon styled and include large collections of characters with animations, monsters, weapons, effects and user interface kits well suited for platform games.
6. Super Game Asset (commercial)
Best for RPG Games. If you are creating your own RPG or isometric games, Super Games Asset store has the highest quality 2D games assets you can buy online. They offer awesome RPG game icons (these are probably the best you can purchase directly online), 2D sprites, character animation sprites, and huge hand painted RPG game maps in isometric view. Majority of game assets here are visually consistent.
7. Open Game Art (free)
The definitive place for open source games. This place is most likely the biggest online community for free licenced game assets. There is a large selection of game assets all submitted under GNU or Creative Commons licences, you can find anything from sprites to icons. It is a great place to start if you are a beginner or just require prototyping game assets. Not all visual styles are consistent though, so you'll need to find and match.
8. Kenny Game Assets (free)
This is another good source for prototyping a game, there are over 20,000+ game assets on this site. It includes various user interface assets, common 2D platform game assets and sprites. Best of all most assets are vector graphics, so it is resolution independent and can be used on any device's screen. Most assets are free to download separately or you can give a small $9 donation to download the whole 20,000 asset pack.
9. Game-Icons.net (free)
best free icon only site, game-icons.net offer a really comprehensive set of icons, in fact over 2000 different variations of monochromatic icons. I say monochromatic because all of the icons here are in black and white but still very generic enough to be used in just about any game. It's a great source to search everything from actions icons, health, potion, character skills, weapons, items. Best of all it's all in vector format.
10. Reiner's Tilesets (free)
Best free tileset site. The game assets on this site are well suited for games with isometric view, Reiner have sprites for animals, plants, buildings, weapons, visual effects and just about every general object to populate an RPG world. The style are more realistic, along the lines of Diablo 2. It is a great place to start game development and test out RPG game engines as all assets are free.
http://www.reinerstilesets.de/en/
This is a good list of assets, but I couldn't help but notice that your website is number 2 on the list and rated as the best source for RPG games. :) You should put in a disclaimer saying as much.