Not always. Colloquially, double negatives are used a lot, especially in phrases involving 'ain't'. In fact, the double negative with a positive meaning is virtually obligatory when using 'ain't. A person who uses 'ain't' would be very unlikely to say 'I ain't been anywhere' : they would always say 'I ain't been nowhere'. This usage is "correct" according to the grammar which governs this non-standard usage. Needless to say, it is not advisable for a non-native to use these forms, unless (a) their English is of a very high level (b) they are among native speakers who are also speaking in this manner.
There are also other cases in standard English where you might use a double negative without it becoming a positive. For example:
'So you said that you don't like that shirt?'
'I didn't say that I don't like it. I said that it doesn't suit me. It's a nice shirt, but it's just not my style.'