When the PlayStation 3 comes out soon, will I still be able to buy PlayStation 2 games, or will they just stop making them ?

It will be like what happened to the Playstation 1. It took a few years for developers & game makers to stop producing games for the PS1 and fully go over to Playstation 2

A game doesn't just appear over a few weeks, some games can take from 9 months to over 2 years to written, tested, marketed & then be released. Major Software companies like E.A. Konami etc have already got PS2 games in production along with new projects for the PS3, as with time they will absorb PS2 games production to be PS3 games and in a few cases they may even completely drop the development of a PS2 game & port it out for the PS3

The PS1 games did go for a fair while after the PS2 was launched and I would expect PS2 game production to drop off mid 2008 making way for the budget titles to appear

I fully agree with Chris here.

I read recently somewhere, that games publishers are actually going to keep making PS2 games for quite a while after the release of PS3.

A LOT of games companies regret that they stopped making PSONE games when they did. They all agree that they could have carried on making them for a few extra years or so.

So, don't worry about PS2 titles suddenly stopping, they'll be around a quite sometime