So you'd like to watch Perry Mason... so you shall.
In 2001 or 2002, when I, in a blur as I swept past the television, first glimpsed Paul and Perry discussing a case, it was early afternoon, one or two pm, and the network broadcasting was FOX. Shortly thereafter we removed house by nearly four hundred miles/six hundred forty-four kilometres and found in our new city that FOX aired Mason at two am—ok by me, an owl by nature. The Hallmark Channel (of US cable television) showed it as well, in the morning, if I remember correctly, at ten or eleven.
The programme has been shifted about, taken off the schedule, popped back in again et cetera many times since then. I'm sure it's on there somewhere, so have a look at the listings in your area.
Or... watch it online! IMDB has some episodes for free, as does Fancast. If you subscribe to Netflix, keep your eye on their Watch Instantly section; at the time of this writing (October 2010) they have only the 1980s/'90s eps, but may add the classics in future. Amazon has a Video on Demand section, where you may pay per episode or subscribe to a series; Perry Mason is not available just yet, however. Their Video on Demand feedback e-mail address is email@example.com—feel free to let them know you'd love to see your favourite solicitor on their site!
I thought that one of the BBC channels showed Perry, but I haven't found anything about it. Perhaps I dreamt it! Lovefilm has the DVDs (as does Netflix), but Perry isn't in their Watch Online section. Beg 'em for it! Amazon's UK site doesn't have Video on Demand just now, although I'm sure it won't be too terribly long before they do.
The above is, of course, just US and UK-specific; my apologies to the rest of the world.
If all else fails (or not)... Bittorrent!