You may probably have a good (or even a decent) connection to the net, but I have a painful 3G connection that lately have been dishing out a performance worse than my old US Robotics 33.6 Modem.
Playing browser based games nearly mandate that you have both a good and stable connection. Stable being a often forgotten keyword. Connection spikes can kill you easier than the challenges you face, even very small spikes can bother you severely.
However, desktop based game tend to be very network-cheap. Civilization can be easily played on a 56k dialup connection, without much hassle. But the latest batch of MMOs are very network demanding, which is the main reason I won't even bother to try them for a good while, even the desktop ones. Devs seem to be only cattering to the very small percent of the gamers that happen to have good connections.