I'm looking for a digital camera that has multiple shot self-timer mode. Is this feature available on mid-range cameras or is just high-end ones?
You can do this with any camera that has a connector for a wired remote shutter release. The vast majority of DSLRs currently on the market have such a connector. You just need a cable release that includes an intervalometer. They are widely available with the various shaped connectors for different camera models. This one comes with various adapter ends that will fit the connector of practically any DSLR on the market. Most include only a specific connector designed for a particular camera manufacturer.
Everything you ever wanted to know about camera remote release connections:
For Mid Range (and high end) Canon DSLRs you can download a piece of firmware called Magic Lantern which does what you described above, and more. I don't use it myself but I've had photographic friends raving about it. The only downside to consider, is that there is some debate whether or not installing custom firmware voids the cameras warranty, so do your research.
I'd say consider looking into it as an option, though personally, I use something along the lines of Michael's solution with an intervalometer.
This is available on quite a few cameras, including even some point-and-shoot ultra-compacts. There is no rule to tell you which model has it, so you must check the specifications on the manufacturer's web site for models you are interested in.
This is a more common option on Canon cameras across the board. Even a tiny Powershot ELPH 115 has that. Olympus makes cameras with that option, such as their Stylus 1. Nikon tends to reserve this for higher-end models, while Pentax and Fuji rarely have it.