cool mock up.
as far as portfolio pieces go and despite the feelings of what some of the other people here may think, I've found that my employers and clients appreciate seeing things from games that they enjoyed playing themselves. like to see sprites that look they are from another game. the first thing i always hear is "have you played such and such game?" or "can you do such and such style?" as it turns out, developers don't have a lot of original ideas. if you work on fighting games, they want to know if you can do capcom style or snk style. if you do space ship games, they've literally sent me screen shots from other games, and told me "make it look like that." for pretty much every game genre out there, expect to be asked to reproduce some other style. make sure your portfolio can reflect that.
you always want to show you have skills that exceed what they will ever need though just to leave a good impression. usually because of limitations set by what platform the game will be for, or who's actually in charge of developing/publishing the game, you will never need to use the full extent of your skills.
developers more often than not are looking for people who can do animations. static sprites with fancy shading and dithering all over the place are great and all, but game sprites require movement. you want to demonstrate that you can animate both fighting game sized characters and low res characters. the majority of the work that is out there will be for GBA or mobile phone so the screen size puts a limit on how big you'll need to make stuff.
another thing I've noticed that people are hiring for lately are little mini game type things. you know, games that involve various puzzles and stuff. for that you want to demonstrate you can make random objects. stuff like orbs, boxes, arrows, clouds, wires, tubes, or whatever other organic and geometric things you can think of.
as far as backgrounds go... that's no really my area, i specialize in characters. but i would imagine though for that you just want to demonstrate you can make versatile tile sets, and create various environments (snow levels, caves, deserts, cities, jungles, forests, grassy fields, mountainous areas, outer space, castles, etc). you want to show you can do layered side scrolling backgrounds, as well as isometric backgrounds.