Short answer: Not a lot.

For those that don't have ESPN Insider, don't try this link, it will just frustrate you that you can't see the rankings, but it's the list of remaining free agents. Two of the best free agents, DE Julius Peppers and LB/DE Terrell Suggs are unsigned, but Suggs isn't going anywhere and Peppers wouldn't be worth the price (money and a bunch of picks back to Carolina). 

ESPN ranks anybody above 70 as a good starter, and over 80 as an outstanding player. Only one unrestricted and unfranchised free agent is above 80, and fewer than a dozen are over 70. Everyone below that level, I'll assume, isn't good enough to start for the Packers. So who's left?

• Grade 80, WR Marvin Harrison. At this point in his career, he's unlikely to have more to offer than any of the Packers' top 4 WRs. That's a knock on Harrison, and it's also a compliment to the Packers' receivers. 
• Grade 79, LT Orlando Pace. Another ex-star veteran looking for work. The Packers already have two veteran tackles, neither as injury prone as Pace. It wouldn't hurt to find a left tackle of the future, but the 13 year veteran's future is now. If he can even stay healthy anymore.
• Grade 75, CB Chris McAlister. Again, recently released ex-star. Again, injury prone. He'll be a lot more help to some team other than the Packers because they already have two healthy veteran CBs in the starting lineup.
• Grade 72, K John Carney. Yes, a 44 year old kicker is the 4th best remaining unrestricted free agent. That should be a giant sign that I've reached the end of it, but I'll keep going anyway.
• Grade 71, WR D.J. Hackett. Another frequently injured veteran who was released recently. At least he was never a star. Some team with no depth at receiver might be well rewarded to take a chance on him, but he makes no sense considering the Packers' deep receiving core.
• Grade 70, LB Angelo Crowell. Finally, a free agent the Packers could consider signing. He's not going back to Buffalo because their coaches put him on I.R. in early September, although he was participating in practice, apparently because they wanted to get rid of him. He's only Plan B in Buffalo. But he's a young, experienced outside linebacker, who may or may not be coming off a season ending injury. He would play at the other outside linebacker spot, and although I'm no fan of LB Brady Poppinga, GM Ted Thompson just gave him a 5 year extension so I doubt he's ready to give up on him. Also, I'm not sure Crowell offers anything more than Poppinga. I'd rather have a better pass rusher at outside linebacker too. 
• Grade 70, QB Jeff Garcia, RT Jon Runyan, TE L.J. Smith. No, no, no. Garcia and Runyan should retire, although neither probably will, and both the tight ends currently on the Packers' roster are better than Smith.
• Grade 69, LB Derrick Brooks and LB Freddy Keiaho. I'll mention them because they're outside linebackers, and the Packers could use a better outside LB than Poppinga, but neither fit with the Packers. Both have spent their entire careers in a 4-3, Tampa cover-2 defense which is completely different than the 3-4, press coverage defense you'll be seeing next season in Green Bay. 
• Grade 69, P Hunter Smith. Sign him! There's a lot to dislike about an 11 year veteran punter who's spent his entire career kicking in a dome. His previous employer isn't too sad to see him go. But the punting combo of P Derrick Frost and P Jeremy Kapinos was so awful last season, that upgrading to an average punter would be huge upgrade. Now I'm depressed that he's the best the Packers could do possibly do in free agency.

It's not glamourous, I'm not even sure it's a better idea then just trying out a dozen recent college grads to see if they could do better. But returning compentency to the punting game is as good as it could get for the Packers with what's left in free agency.