I collect Superman figures, Figures Toy Company Mego reproductions, Hot Toys figures based on comic movie characters, and anything that catches my eye. Right now, the figures are displayed in cases (just plain book cases), but I am running out of room.
I like to collect figures and statues based on Christopher Reeve Superman out of nostalgia and it reminds of being a little kid in awe of the Superman movie. I like the Henry Cavill Superman figures because I enjoyed Man of Steel and I believe he is great as Superman. I have 50-60 Superman figures and my favorites are the Hot Toys Superman figures. Yesterday I received the Barbie Black Label Henry Cavill Superman figure. Also have the Mego 12 inch Superman from the late 70s. He is still in the box. I have the Mego 12 inch Wonder Woman too, still boxed.
From Hot Toys I also have Star-Lord, 2 Hugh Jackman Wolverine figures, and I've pre-ordered Quicksilver and Scarlet Witch.
I have both Arrow statues and several of the figures that tie in with his show.
I like the Figures Company figures as they bring back happy childhood memories!
I enjoy these figures and statues because of the happy memories they bring back and I like to look at them. Also have around 20 or so of the DC Direct mini busts.
Mainly, I just collect what I like. It is a fun hobby and it's nice to see so many favorite characters being aimed at the older collector who has enjoyed the characters for years and years.
If the figure is well made, is pleasing to the eye, and not too terribly expensive....I am a sucker and will purchase it.

When I was an adolescent, action figures were my creative outlet. I'd pull out my Marvel Superheroes, my Kenner Super Powers, and a few other toy lines, and I'd start developing complex plots, backstories, and characterizations that had very little to do with the comics themselves. It was my preferred means of expressing myself creatively.

As I grew older, I got into other creative outlets: writing, drawing, and a few other things, but with each of these came a sense of expectation. Was I going to publish my stories and poems, get good enough to pencil for a comic book company, and so on. These expectations ensured that, the better I got at these hobbies, the less of an outlet they became. These days, my number one outlet is reading and discussing comics and classic films, but I still enjoy having a room full of vintage toys from my youth, and a few times a year, I'll pull some down and enact a full fledged epic with them.

So for me, collecting toys is one part nostalgia, and five parts "that would be really fun to incorporate into a story sometime down the road!". I open all of my toys and don't worry much about condition beyond it looking "nice enough" and being intact. About ten years back, when I was buying up much of my collection, I was a mid-range ebay seller, so I bought, sold, and ended up making back much of what I spent on toys. Back then, condition mattered more.

I collect anything that either reminds me of the fun I had playing with toys as a child or that would fit in well with those toys. So generally 3.5" to 5" Marvel, DC, Star Wars, and Star Trek action figures, vehicles, and playsets, as well as LOTS of transforming robot toys (Transformers and others).

I display them so that they maintain eye appeal to me and make me happy to see them. Nothing more complex or logical than that.

I really like the figures based on the art styles of specific artists (Greg Capullo, Darwyn Cooke, etc). I have a few of the Greg Capullo ones, and they're all pretty nice (especially the huge armor suit Batman; it's very well-made, and appeared in one of the first Batman comics I ever read). I'm not a huge Jae Lee fan, but the figures I've seen at my LCS seem to capture his style pretty well, too. I'm looking forward to future lines of these figures.

I have an increased interest in DC's Elseworlds books lately, so I'm considering collecting some of those figures as well. The first one is on the way now, so I'll see whether I like them or not. If I like that one, I'd like to get the JSA: Liberty Files Batman at some point. I haven't read that book yet, but I really like the design of the character.
Edit: Never mind about the JSA Batman. I just checked the prices, and it's about $130. That's a little pricey for me. Maybe it's because of his resemblance to the one Batsuit from Batman vs. Superman? 

I don't know. I don't think it was a limited release, but it is about 10 years old, I think, so maybe they're in low supply now. The other figures in the line have much lower prices (fortunately for me, as I recently ordered the Gaslight Batman ). 
I hope it drops in price sometime, as I really like the design. How else can I re-enact Countdown: Arena #1, where the JSA and Gaslight Batmen fight?  
Edit: I just saw a comment on a youtube review of the figure that says the figure was available for $26 unopened when that comment was made, which was a month ago. Apparently there has been quite a rise in price in the past month! I wonder if that was due to the similarity to the BvS Batsuit, or for some other reason?