Here's a few portfolio sites that really stood out to me in my research of like sites. In doing the research, I actually learned more about what I want my website to look for judging by what I am attracted to with design. The sites that are heavy with flash/pictures/moving images or animations are not the style that I am going for. The portfolio sites that are text-heavy and rich with simple design are the ones that catch my eye and will be what I base my redesign off of.
To start, let's look at jeffsarmiento.com. He's a web designer with a graphical, yet clean looking web site. I don't know how I feel about his custom drawings of underlining and arrows and you can see next to the "flickr" logo and the "we have lift off" graphic. I think it's cutesy and I'm not really going for cutesy -- I'm going for a look that says, "here's a professional recent grad who is serious about a career in ______ " (I'm not saying that Jeff's site doesn't say that -- but if it does, it's cutesy).
I like that he has the vertical menu bar positioned on the right side. This to me was "unexpected" as fred outlined for us as something to strive towards (I hope). I am beginning to agree more with this "unexpected" take because I feel like out of all the portfolio sites I looked at, nearly 90% had the menu bar vertically positioned on the top of the site and it remained there throughout the site.
Again, keeping with his cutesy nature, Jeff has custom graphics next to each menu bar item along with a changing rollover color (which stays put while on each respective page). I am impartial to the idea of a color change, but I know I wouldn't want this many colors on my site.
Check out jasonreeddesign.com. It's not one of my favorites, but there are some things that I like and find interesting in his design. Though it may be a tad narcissistic, the idea of a logo being your signature is kind of neat. It looks professional, in a way, and can almost give you a sense of his personality. I mean, people who study people's handwriting and would tell you that you can get a true sense for a person just off their style of writing and signature. With that said, I like the contrast of his signature with the typography and it works well with the drawing of him.
This happens to be the only design aspect I like on Jason's site. I don't care for his interface (each page kind of flips by like a card in a stack) and I don't think his social media links are prominent enough.
digitalmash.com is a prime example of a site that solely uses typography and it is still visually appealing. I like the typography and color scheme and although it can be confusing/unclear as to what you should click or what exactly you are clicking on the colored links, the basic nav bar on the top right will bring you to more cohesive and organized links.
When you do click a link, it stays its respective color and the rest of the links dim to light gray and you are brought to the page (as seen below). I like how the links and the one colored indicator link remain at the top as a sort of header and design element. This site is really well done, in my opinion.
markboultondesign.com uses another typography rich angle of design and is, again, incredibly effective while remaining visually appealing and professional. Besides the pumpkin/sweet potato color choice (I think it's forgettable), I like the header, with the oversized "De Standard" as the background to the nav bar and logo. With that said, I think it can be confusing to find the nav bar right away, though when you rollover the links, you get a nice, cream colored box that comes up behind each link to make them easier to read and more enticing to click, I think.

I like Mark's portfolio page, again heavy with text and minimal with graphics, I think it looks professional and I like that they did not keep the oversized "De Standard" as the header throughout the site. This idea kind of sparks some interest in me when thinking about the design of my own site. It would be interesting to play around with a design where the homepage header is lager (perhaps more visually enticing) and then downgrades to a simpler nav bar and logo on the rest of the pages on my site.
As I mentioned before, exploring and critiquing other successful portfolio websites has helped me garner more of an opinion and a few ideas as to what I want my website to look like.