Some folks have removed the edge banding and replaced it with veneer edge banding stained to match or with a pvc edge banding. It's a fairly simple process, although somewhat time-consuming. The results are definitely worth it, though!
[BREAK=Take it off!]
Edge banding is removed using a household iron and a thin kitchen towel. Set the iron to a medium setting and place the towel over the edge banding to be removed. Run the iron over the edge banding for about 30 seconds. The edge banding should peel right off.
Replacement edge banding can be purchased at specialty woodworking stores, such as Rockler or Woodcraft. You should also be able to buy the tools to trim the banding to fit and find a knowledgeable salesperson to help you find a stain to match your door style if you don't find a match listed below. Some people have used a mix of several different stains to achieve the look they wanted. If you need a melamine finish, you may have to widen your search to include internet sources.
[BREAK=Give it a new ]
Follow the directions on the edge banding packaging to apply the new edge banding and trim it to size--there are special tools for this exact purpose including a double trimmer. A standard exacto blade with some patience and a steady hand can be substituted.
Standard pine moulding and decorative accents can be used and stained to match as well. Check below or in the article
Finish Matching: Stain and Finish Matching for IKEA Cabinets for stain formulas--unless otherwise noted, assume white pine as a standard base wood.
[BREAK=Known Matches]
Known Matches:
Hallarum: Mahogany Veneer (darker of heartwood or sapwood) / Mix of Early American and Shaker Maple water-based stains by "EF Finishes by General Finishes" or Minwax Red Mahogany on red oak edgebanding
Adel Cream: Plastic Edgemate in Almond from Rockler
Nexus Brown Black: Edgemate in Black
Adel Medium Brown:
White Birch veneer edge banding with General Finishes' Gel Stain in Candlelite. Apply one generous coat -- one coat is too light, 2 coats are too dark. Excess wipes up easily