The other comments here are very valid if you're looking for that spontaneous photograph. I often use the drive-by shooting technique to get that unposed look. Get in there though, so they can see you regardless. Act like you belong there. Do not skulk about. After you've done it a few times, you can discard your 50mm and get right in there with a 20mm...
But seeing as you asked about asking people, that is exactly what I do; ask them.
As soon as you see an interesting subject, do not hestitate, walk straight up to them and ask. I do this regularly. If they ask why, you say, 'I am a photographer'. 99% of people say yes to me. I also have a business card to give them before/after to cement the sale.
Sometimes it works, other times they go all stiff and you can see the business card you gave them, or their cat will not sit still... But when it comes off, you can get some great work.
Like Susan says, ask first if you want a street portrait. They are often worth the effort. This is of course what sets apart a photographer from a tourist with a lazy long lens, which generally pisses people off as it is obvious you're a gutless sneaky type.
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