Originally Posted by
Throbert McGee alexnoel: I'm not a native speaker of Russian, but I think your translations are essentially correct.
помнить (imperfective) is the most basic and non-specific verb, and doesn't have a perfective with the same non-specific meaning
вспоминать/вспомнить suggests that you're making a concerted effort to pull up something from long-term memory, or possibly that you're nostalgically reflecting on something that happened long ago
запоминать/запомнить is "to memorize; commit to memory"
напоминать/напомнить is "to remind" (as in "Remind me about the meeting tomorrow"), but also "to be reminiscent of; to resemble" (as in "I don't know what this food is, but the flavor reminds me of bacon")