My experience is mostly that your computer will start to freeze /blue screen etc. I will explain why that happens below for anyone who really cares. The only computer's I've heard of actually going up in flames was a result of dust built-up probably accompanied by insufficient airflow to begin with. I've certainly burnt my finger, checking the temperature of hot chips... touch something grounded (for static) before trying that at home though.
In computer engineering we have registers which remember values from one clock-cycle to the next. We learn there's a propagation delay during which the logic is not yet stable, your CPU from the factory is clocked for the worst-case. Not all operations take the full amount of time, so when you overclock your CPU just a little bit your system should mostly continue to work reliably (which is what you're betting on when you overclock a chip). In most cases the occasional incorrectly calculated value will not be noticeable to a user, I don't think it's a big risk while playing video games for example.
I would highly recommend against overclocking a CPU while installing new software or drivers, or while defragmenting your disk (which late versions of windows does in the background). That being said I've also heard that the Celeron brand was largely the same (with possible quality differences) as the Pentium brand (both intel products) but then again I doubt very many people would bother to overclock a cheaper chip when a quicker one is not that much more expensive. These days the CPU is no longer the bottle-neck it use to be, and you will gain a lot more speed from an SSD, more RAM, or a good GPU.