Maze Generation

Mathematica, 144 132 bytes

Since Inception, we all know the most efficient way to draw a maze.

c=0;Graphics@Most[Join@@{Circle[{0,0},i,{a=c-(r=Random[](d=2Pi-1/i)&)[],a+d}],Line[{{i},{i+1}}.{{Cos[c=a+r[]],Sin@c}}]}~Table~{i,9}]

Ungolfed and example output:

Of course, the lines are the walls. You're the minotaur who starts in the centre and needs to get out.

C: 364 Bytes

#define I int
m[1600],i=0,r;f(I x,I y,I l){m[80*y+x]|=l;I d[]={x-1,y,2,1,x+1,y,1,2,x,y-1,8,4,x,y+1,4,8},
s[]={5,5,5,5},j=0;for(;j<4;){L:r=rand()%4;for(I k=0;k<4;)if(s[k++]==r)goto L;s[j]=r;I*p=d+
4*s[j++],X=p[0],Y=p[1];if(!(X<0|X>79|Y<0|Y>19|m[80*Y+X])){f(X,Y,p[2]);m[80*y+x]|=p[3];}}}
main(){f(0,0,4);m[9]|=4;for(;i<1600;)putchar("#5FMP<HJR;IK:9LN"[m[i++]]+128);}

Note: in the above, I added newlines to make it fit on the page. Expected output (on 80-character terminal) (note start and end at top left):

Mathematica, 134 130 chars

Graph[Range@273,Reap[Do[c@n/._c:>#0[Sow[#<->n];n],{n,RandomSample@AdjacencyList[g=GridGraph@{13,21},c@#=#]}]&@1][[2,1]],Options@g]

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In fact, we can use this algorithm to generate a maze from any (undirected) graph.

For example, generate a maze from the 8*8 knight's tour graph (KnightTourGraph[8,8]):

Graph[Range@64,Reap[Do[c@n/._c:>#0[Sow[#<->n];n],{n,RandomSample@AdjacencyList[g=KnightTourGraph[8,8],c@#=#]}]&@1][[2,1]],Options@g]