Both are possible. Generally speaking students are taught that we only use 'any' with either plurals of countable nouns or uncountable nouns. So if you were having a meeting and you wanted to ask your colleagues for their thoughts you would say 'any suggestions'. However, we do sometimes use 'any' with a singular noun (such as 'suggestion'). Normally people do this to make a specific point, and when spoken the word 'any' is stressed (emphasised) to make this point clear. Imagine you have spent several hours with friends trying to choose a film to watch and one friend keeps saying 'no' to all the films and hasn't made any positive contribution to the conversation, you could say 'any suggestion'... As in 'any type of suggestion' See this link for a longer explanation http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv303.shtml

Do you have any suggestions? Reason: any (singular); suggestions (plural) ....any one of the suggestions.

You can also say, 'Do you have a suggestion?'