When I first started, I disregarded anything below 80 searches a day. Anyone who has done the 30DC/Challenge will know of the criteria they use and it's perfect for beginners.
These days, I target every single keyword in my niche regardless of search volume because in my experience, data is more a guide than proof positive of the traffic you will receive.
You also need to factor in the intent behind the search. Some low volume search phrases convert extremely well, some high volume searches don't convert at all.
For example, I have a page dedicated to a search term that according to Google, gets 11 exact searches/month and I typically receive 5-6 visits/month (I am ranked first but below an Adwords block). This is a product review search and my affiliate pays $84 per sale. I have an article as well as a video that reviews the product. I have sold at least 1 per month from this low volume but highly converting search phrase.
Another thing you need to take into account is how the search phrase or keyword is trending as well as the broader market it belongs too.
For example, let's say we have a keyword that receives 100 searches per day. Using Google Insights, we can check the history of this keyword and see if the keyword and broader market it belongs to is trending upwards or downwards. This works well with low volume keywords as well because you can tell if it's going to grow over the next few years or if it's losing search volume year on year.