Is it wood or mdf?
If it's mdf, don't use any water. MDF will swell irreparably when it gets wet, and it won't be pretty.
If it's wood, there's no easy solution. Use a razor or stiff putty knife to carefully scrape as much as you can off. Then try to dissolve the residual glue with a rag and a solvent. I'd try these in order of increasing potential damage to the underlying paint: mineral spirits, isopropyl alcohol, turpentine, acetone.
If none of it works, (it will, though), roll up ya sleeves and get outcha sandpaper.
If that doesn't work, rent a jack hammer and position it against the wall carefully where the offending tape refuses to yield. Plug in hammer. In your best Rebel Yell, cry out "D@mn you, 3M!" and go Rambo on your wall.