Orange color schemes combine the warmth of red with the happy brightness of yellow (= the colors that 'make' orange). The color orange is the warmest hue on the color wheel chart, and it has an upbeat, positive, sunny vibe.
The following orange color schemes make good room color combinations (more great color combinations here):

Pale oak + icy blue + teal + palest mauve + rust
↑ This is one of the best orange color combinations for retro decorating (as well as retro fashion!): The grayish mauve and pale oak are essential for a 'vintage' look, but if you decide to leave them out you end up with a great color combination for a rustic seaside/mountain home. (Here's a contemporary living room color scheme in a similar vein!)
Best wall colors: White, pale tan or manila beige.
Best wood stain: Natural oak.

Black olive + orange + green olive + stone + cobalt blue + chartreuse
↑ Inspired by Mediterranean cooking & culture, this yellow-orange color palette with intense cobalt blue and zesty chartreuse reflects some of the visual 'flavors' of Southern France. It would look gorgeous in a modern, Mediterranean style kitchen. The 'stone' color makes a good neutral background hue. (More French country colors here!)
Best wall colors: Palest yellow-orange or stone. An accent wall in full-on orange, or olive, or even cobalt blue would probably not go amiss.
Best wood stain: Dark walnut.

Delft blue + cream + ivory + terracotta
↑ This blue-orange complementary color combination is one of the easiest, most satisfying orange color schemes I know. 'Earthy' orange also co-ordinates beautifully with French blue, cobalt blue, or royal blue. For variations of this earth tone color scheme, try replacing the color orange with related yellowish or reddish earth colors, e.g. red ochre, yellow ochre, raw sienna, or burnt sienna.
Best wall colors to go with this earth tone color scheme: Soft terracotta, cream, pale misty blue.
Best wood stains: Oak, rustic pine, or really deep dark browns.
The orange/hot pink color palette is fabulous for summer weddings, and you'll find several versions of this color scheme further down. Here's a combination of deep orange and pink wedding colors:

Deep orange + fuchsia pink + pale pink + leafy greens
With palest, chalky pink on the walls, you could use these strong colors even in a room color scheme - imagine a striking orange bedroom color palette focused around, say, a quilt in orange, fuchsia and deep greens.
Best wall colors: Palest pink, gray, chalky sage green.
Best wood stains: Dark hardwoods.

Misty blue + orange + hot pink + bronze
↑ As a twist on the orange and pink color scheme above, here's a vibrant color combination with orange that plays off two warm colors (orange and pale bronze) against a cool misty blue and a rather cool (=bluish) 'hot' pink. It's an 'exotic' color scheme that looks great under a bright Southern sky!
Best wall colors: Pale orange, a pale blue tint, or very pale bronze.
Best wood stains: Dark hardwoods.

Dusty turquoise + pale lime + teal + orange
+ tangerine (= red-orange) + aqua + verdigris
↑ This blue-green-orange palette would make an upbeat, "year-round summer" room color scheme. It looks good on textiles for a summer house, veranda, deck, or garden furniture. It combines orange with a range of analogous blues and greens from the opposite side of the 3-primary color wheel.
For a simpler version, use just one half of the combination above:

Orange + teal + dusty turquoise + lime green
↑ The left side of the 'Garden Party' color scheme is a warm, 'citrus' color scheme of orange & lime green, with added blue-green tones. It would make a nice, juicy kitchen color palette. (If you find it too warm, add more aqua or turquoise to cool it down.)
Best wall colors: White, pale apricot, light chalky lime green.
Best wood stains: Any.

Aqua + verdigris + pale aqua + tangerine
↑ Here's the right side: another very popular wedding color scheme which is essentially a blue-orange complementary combination with an added dash of slightly bluish green. The aqua hues serve to cool down the intensity of red-orange.
Best wall colors: White, or translucent aqua (if it's a sunny room).
Best wood stains: Limed oak or dark hardwoods.

Sea glass + apricot + winter white + spicy chocolate + cool grey
↑ For an elegant, modern orange-green color scheme, look no further than this one: Duck egg blue or 'seaglass' make beautifully timeless orange color schemes. The soft apricot and blue-green tints make it perfect for a bedroom or a living room in orange color. The deep, slightly reddish brown adds more depth and warmth to the color palette.
For a subtly cooled-down version,
Best wall colors: Pale apricot, frosted seaglass (or palest aqua), warm white
Best wood stain: Antique mahogany.
Plus, here's some additional color inspiration you may want to look at:
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