In reality, there's a limit because the controller chip must store the entire LED strip pixel data in memory. Each pixel takes up 3 bytes. For an Arduino Uno (or other '328 based 'duino), the processor has very limited memory, that means that you can't really run more than 250 or so pixels. That number is a little dependant on what else the Arduino is storing - for example the SD library takes up a massive amount of RAM memory. In our experience, most people have issues with over 150 pixels.
There is no easy way to check runtime RAM usage (unlike the FLASH storage which is printed out on compilation) so if you're having issues with longer strips, shorten the strip or update to a Mega which has tons more RAM.
There are a few things you can do to minimize RAM usage. Minimizing string usage is often a good place to start. This page has some good tips: http://itp.nyu.edu/~gpv206/2008/04/making_the_most_of_arduino_mem.html