ASCII Box rendering

APL, 116 bytes

{⎕IO←0⋄K←' '⍴⍨⌽+⌿2 2⍴⌈⌿↑⍵⋄K⊣{x y W H←⍵-⌊.5×⍳4⋄K[Y←y+⍳H;X←x+⍳W]←' '⋄K[Y;A←x+0 W]←'|'⋄K[B←y+0 H;X]←'-'⋄K[B;A]←'+'}¨⌽⍵}

This is a function that takes an array of arrays and returns a character matrix.

Tests:

      t1← (0 0 11 4)(8 2 8 4)(3 5 8 3)
      t2← (0 3 11 4)(8 5 8 4)(3 8 8 3)(4 0 13 5)
      t3← (⊂0 0 2 2)
      t4← (2 2 5 3)(1 1 7 5)(0 0 9 7)
      {⎕IO←0⋄K←' '⍴⍨⌽+⌿2 2⍴⌈⌿↑⍵⋄K⊣{x y W H←⍵-⌊.5×⍳4⋄K[Y←y+⍳H;X←x+⍳W]←' '⋄K[Y;A←x+0 W]←'|'⋄K[B←y+0 H;X]←'-'⋄K[B;A]←'+'}¨⌽⍵} ¨ t1 t2 t3 t4
┌───────────────────┬─────────────────────┬────┬───────────┐
│+---------+        │    +-----------+    │++  │+-------+  │
│|         |        │    |           |    │++  │|+-----+|  │
│|         |----+   │    |           |    │    │||+---+||  │
│+---------+    |   │+---------+     |    │    │|||   |||  │
│        |      |   │|         |-----+    │    │||+---+||  │
│   +----+------+   │|         |----+     │    │|+-----+|  │
│   |      |        │+---------+    |     │    │+-------+  │
│   +------+        │        |      |     │    │           │
│                   │   +----+------+     │    │           │
│                   │   |      |          │    │           │
│                   │   +------+          │    │           │
│                   │                     │    │           │
│                   │                     │    │           │
└───────────────────┴─────────────────────┴────┴───────────┘

Explanation:

• ⎕IO←0: set the index origin to 0.
• Create a matrix of the right size:
  • ⌈⌿↑⍵: find the largest values for x, y, w, and h
  • +⌿2 2⍴: x+w and y+h
  • K←' '⍴⍨⌽: make a matrix of x+w*y+h spaces and store it in K.
• Draw the boxes into it:
  • {...}¨⌽⍵: for each of the boxes, in reverse order,
    • x y W H←⍵-⌊.5×⍳4: assign the coordinates to x, y, W, and H, and subtract 1 from both W and H. (coordinates are exclusive, APL array ranges are inclusive.)
    • K[Y←y+⍳H;X←x+⍳W]←' ': fill the current box with spaces
    • K[Y;A←x+0 W]←'|': draw the vertical sides
    • K[B←y+0 H;X]←'-': draw the horizontal sides
    • K[B;A]←'+': set the edges to '+'
  • K⊣: afterwards, return K.

ES6, 228 223 217 208 201 198 bytes

Accepts an array of arrays of coordinates and returns a string.

a=>a.reverse().map(([x,y,w,h])=>[...Array(y+h)].map((_,i)=>(s=r[i]||'',r[i]=i<y?s:(s+' '.repeat(x)).slice(0,x)+(c=>c[0]+c[1].repeat(w-2)+c[0])(y-i&&y+h-1-i?'| ':'+-')+s.slice(x+w))),r=[])&&r.join`\n`

Where \n represents a newline character.

Edit: Saved 5 bytes by reversing my conditions. Saved a further 6 bytes by switching from an array of char arrays to an array of strings. Saved a further 9 bytes by introducing a temporary variable. Saved a further 7 bytes by introducing a helper function. Saved a further 3 bytes by undoing a previous saving!

Ruby, 153 143

->n{a=(0..m=3*n.max).map{$b=' '*m}
(*n,x,y,w,h=n 
v=w-2
h.times{|i|a[y+i][x,w]=i%~-h<1??++?-*v+?+:?|+' '*v+?|}
)while n[0]
a.delete($b);puts a}

Ungolfed in test program

f=->n{                                #worst case width when x=w=large number, is max input*2+1
  a=(1..m=3*n.max).map{$b=' '*m}      #find m=max value in input, make an a array of 3*m strings of 3*m spaces 
  (
    *n,x,y,w,h=n                      #extract x,y,w,h from the end of n, save the rest back to n     
    v=w-2                             #internal space in rectangle is w-2  
    h.times{|i|                       #for each row
      a[y+i][x,w]=                    #substitute the relevant characters of the relevant lines of a 
      i%~-h<1?                        #i%~-h = i%(h-1). This is zero (<1) for first and last lines of the rectangle
      ?+ + ?-*v + ?+ :?| + ' '*v +?|  # +--...--+ or |  ...  | as required
    }
  )while n[0]                         #loop until data exhausted (n[0] becomes falsy as it does not exist)
a.delete($b);puts a}                  #delete blank rows ($b is a global variable) and display