Separation of "need for work" and "nice to have for leisure"
Regardless of the trend I've heard in IT news lately that the number of personal devices on work networks are on the rise... for the moment, your cause is better served by separating the need for sites that help you solve problems (like blogs on technical topics) and sites that provide services that help you balance your work and personal life (Gmail).
There IS a justifiable concern about personal email out there from a security perspective, and there's not a lot of footing to say that you have a right as an employee to use work resources for personal business. There has always been a flex in the work place around this sort of stuff, but at the moment, the tide is swinging in the other direction.
Mixing these two needs together will weaken your cause talking to the higher-ups.
Know the Blocking Process
OK - looking just at blogs, which do help solve technical work problems...
First, see if there's a way to easily separate the good from the bad. For example, I find a significant number of tech blogs that are useful are hosted by word press. Not so many are on LiveJournal. A few are independantly hosted and these are usually not the problem. Get yourself clued in on the nature of the hosting of the blogs you need the most.
Also - check in with IT and see what you can learn about the blocking process? Is it by domain? URL? IP address? Category? Do they have the capability or intent to allow certain types of users? Ever?
Be ready to work within the capabilities of the tools they are using. I can feel confident asserting that there is a technical way to grant an expection (every place I've worked has had a way) - but that there may be limitations on why they won't. Before starting the battle, understand the limitations.
Stick to the work - build a case
Figure out what the limitation is when you can't get the information? Is there another place to find it? Why are blogs better than other resources? What is the penalty imposed when you can't get the information? Be ready with good cases from the pre-blocking time. Stay away from vague references or hopes for the future. You need an actual case where a blog helped get work done better.
Know the tradeoffs between what you want, and what IT wants. Figure that there is a justifiable cases that they have to be fair - if you get a waiver, so should others - are your needs consistent and consolidated enough that you can help write a policy that makes sense across the board?
Cycle it through with your bosses.
This is not the kind of endeavor your boss wants to hear of after the fact.
But you can kick off the discussion with your boss in the framework of "I have a problem, I have an idea for a solution, what I can do to move forward with it?" which is almost certainly more productive. This is where knowing the real business impact, and sticking to only the sites that help with work is crucial. If it seems like you are trying to just help yourself, you won't get buy in.
Agree with the boss on how to approach this idea, and the move forward keeping him in the loop. Be prepared for a "no", but be ready to challenge it with "then how else should I find this information?" Be ready to point out that mixing work and personal life by surfing for these blogs on your phone is not the answer, either, as the form factor can be painful, and we're blurring the line, again, between work and home life.
You may not win this one - I know I haven't always won this particular battle. I've managed certain kinds of blocking exceptions, but there were times where download of certain open source tools were so debilitatingly impossible, that I actually left the company because I truly believed there was no investment in success of key business objectives.
But when I want this kind of change here's my step by step process:
1 - identify exactly what I want to get un-blocked
2 - identify why it's killing my productivity and why it impacts more than just me.
3 - have an informal chat with IT and find out their limitations and issues
4 - prepare a proposal
5 - meet up with my boss, look for consensus
Is it your job to fix the problem? No, but you really have two choices in any situation like this - try to change it or accept it. I think if you stick to the things that slow down your work, you have a good chance of at least being heard, if not actually getting what you want.