Mobile devices are quickly becoming the go-to platform for gaming. The good news is that the web browsers in most of these devices are pretty good, and in most cases, you can make your mobile game run smoothly on them.
These devices have, however, some memory and power limitations. There are some games that simply won't work on a mobile browser at the moment. You cannot expect to have just as many sprites running smoothly on your smartphone that has one-tenth of the power of your desktop computer.
On the plus side, a mobile device offers a few capabilities you typically don't find on a desktop:
The multi-touch interface allows for new kinds of interaction with your game
The device orientation API allows you to control your game or UI in interesting ways
Most devices allow your game to be installed to the "springboard" just like a native app, blurring the line between browser games and native ones
An offline cache allows your game to work even without an Internet...