You're doing it wrong.
Generally, there's an "other way". The answers to this question are all great, but honestly, you should look at all the different option. Squeezing as much text in as little space as possible always means you've botched a previous design choice.
- Perhaps you should have flipped them to be horizontal bars, giving you WAY more space to work with.
- Perhaps you shouldn't have gone with a bar chart, or shouldn't have gone with charts in the first place.
- Perhaps the problem is the actual data, and you might've had to split it up even further!
- A side-bar or legend/index could help
- Hovers might work for the online version
There are so many options, make sure you use the right one. Squeezing as much information into a single small area as possible is always the wrong way to go. Information needs space to breathe, to be readable, to be scannable and recognizable.
Yes, this generally means using way more space. But that's not a bad thing. It will take less effort for the person who consumes the data to quickly scan a couple of pages filled with well-structured information, than to figure out what that one bar means on that one-page-report. Think of the old board member, pocketing his reading glasses while passing the paper to the person next to him: "I can't read this - what does it say?"
Apologies for the harshness and slight tongue-in-cheek title, but I see that top answer and just feel that the "needs a different approach" part needed more elaboration.
.edit:
Since this is a very contested answer, and fairly conflicted with the original question, I feel I should elaborate on the reasoning behind posting it.
The question that was asked was, in a way, dubious. "Name [X] fonts that are readable at small sizes". While it was probably not intended as such, it does seem likeFirst off: this isn't a trickUX question at worst, a loaded one at bestit's graphic design or typography question.
There are assumptions in this question, the biggest one being that the "correct solution" to this UX issue is small text. But it's not. Small text becomes unreadable, an issue aggravated by tablets and other mobile devices. What if your user has bad eyesight? What if it's shown on an older, lower resolution monitor? What if there's glare from the sun or a light? So many reasons why small text can be unreadable.
As such, this answer is here to help the next person that has this issue to be mindful of not making the same mistake.
... having said that - I totally appreciate that the person asking the question simply doesn't have resources for anything but a font-change :) We've all been there, and we'll all be there again!
TLDR: I treated this question the way Henry Ford treated the call for faster horses. (Disclaimer: I'm not Henry Ford)