Depending on what source you're watching, it may be only that one story that's black&white, or there may be a few others. All episodes were made in colour starting with the Third Doctor. The problem lies within the BBC Archive. They purged their library in the mid seventies of old programs, which is why many First and Second Doctor stories are gone, and many Third Doctor episodes only exist in black&white.
However, the Restoration Team has been recolourising the black&white episodes, in most cases working from a low-quality colour print (typically an NTSC videotape from the American rebroadcast) along with a high-quality black&white. So far, "Doctor Who and the Silurians", "Inferno", "Terror of the Autons", "The Dæmons", "Planet of the Daleks" and "The Ambassadors of Death" have been restored and released on DVD, and "The Mind of Evil" will be released in June 2013. An attempt at restoring colour to "Invasion of the Dinosaurs" episode 1 was made, but failed, so the DVD release remains B&W (though the attempt at colourizing is also included). (Everything else either was never lost, or was later recovered.)
If you're not watching the DVDs, you'll have a different set of black&white episodes. There were some (generally lower-quality) restorations released going back to the early 90s, and some of the restorations have been rebroadcast, so if you've got, say, a VHS collection a friend lent you that he got by trading with other fans over the years, it's hard to guess which ones you'll see in colour and which you won't.
In relation to the first Third Doctor story, "Spearhead from Space", it should also be noted that it was the first and only classic-era story to be completely produced, top to bottom, on film. Therefore it was the only story not subject to "wiping", so there was never any issue of only a black and white version surviving, unlike the video/film production mix of the others.