Unicode Blocks
Using Unicode we can probably create a much better looking blocks, the problem is finding the correct characters to use, I have found a few possibilities using this site. We also have to be careful to use single character width characters.
Player
These are some ideas for the player, but they aren't quite right.
Top
o
๐พ
โพ
โ
โ
๐
๐๐๐ต๐ฃ๐ฑ๐ต
(Maybe the player can have different states: expressions, move arms, legs etc...)
Bottom
ฮ แดง
แฑ ^
โดท โ
โ ๐
๐ก ๊
ส ฦ
ษ
โ
โง โป
๐ค โต
โณ
This would be nice, but not really going to work: ์.
(Hand (Cursor): โ) :P
Grass
โ
๐ค
~
โ
โ
แจ
แ
เทด
โ (Current)
Ores
โ ซ โ
โท โซ
แข ๐น
โข โ
โฃ โ
๊ โด
โต โ
๊ท โฆ
โข โข
Leaves
โง
โ
โป
โ
Sun
Maybe this could be used to make the sun circular: โฌค. It is two characters wide, which will cause problems, but maybe we could use something like a ZERO WIDTH SPACE to offset the characters after it.
We will have to do something odd to make it work, because it will only be able to use characters when there are no other characters in the foreground. So we might end up with square corners when the sun is over a transparent fg block.
Pickaxe
Currently this โ. A better character is this โ but it has worse support. They are both more than one character wide but this doesn't matter too much because the grid borders are less than a character wide.
There are a good selection of characters here including some for the sun โ.