I said my previous salary was $100 and i wanted $110. Previously in the interview I stated I wanted to come in between 105 - 110.
The offer came today and it's over the midpoint at 108.50.
Since they came in just below my asking, is it worth negotiating with them?
Well, they didn't come in below your asking. Regardless of your last number of $110, you did say you wanted it to come in between $105 and $110. $108.50 is in that range, so that is not below asking. They actually probably think they're being generous: you gave them a range, and instead of picking the low end, or even the midpoint, they gave you a little more than that!
Unfortunately you anchored your expectations by giving them a salary range, and they went ahead and fulfilled your request. It's better to avoid giving numbers at all (let their first offer to you be the first time a concrete number is uttered), but if you must, don't give a range. Give a number that you actually want. If they fail to meet it, and you decide to negotiate, they shouldn't be surprised.
Regardless, you can always negotiate. It's exceedingly rare for a company to rescind an offer simply because you decided to negotiate. (Consider that they've likely spent tens of thousands of dollars of their time and resources interviewing you and others for this position; they don't want to repeat it.) They'll likely be a bit confused, since you gave them a range, and they met it, but it likely can't hurt to try.
"Thank you for putting together a great offer, but I was really hoping for that $110 figure I mentioned. That would really help me because X. Is there anything we can do here?" While you don't technically need to provide a reason, doing so will often make the recruiter want to help you more. Acknowledging the work they put into the offer shows respect for their time.
If they respond in the negative, you can also suggest that a higher signing bonus, or some other form of compensation (be specific as to what), would also work for you if it's a possibility.
You can also sweeten the pot by giving them your commitment: after saying the above, finish with, "If you can meet my $110 figure, I'd sign on the spot". This gives them a concrete way for them to "win" you. Of course, only do that if you'll actually sign if they meet your terms. Giving them a commitment and then backing out on it might actually cause them to rescind the offer, or at least to cease trying to meet your needs.