I've always used the colored numbered plastic leg bands.  Sometimes the birds do get them off, but I put one on each leg so I've never had them get both of them off at once.  I just replace them when they fall off.  I've had two birds get them down to the foot but not completely off, and one bird get it stuck up high on the leg, so I check every bird every day to make sure the bands are in place properly.  None of these three birds were seriously injured by the band getting stuck in the wrong place, but would have been if it had not been removed soon.  I probably wouldn't use them in birds that weren't individually observed daily, or birds that can't be easily caught, for that reason.
 
The only other problem I've had with those bands is that I don't always get them placed right the first time.  The bands have overlapping ends, and have the same number printed twice on the band.  If you overlap the wrong end on top when you place them, the second number is hidden and you can only read the number from one direction.  That can be inconvenient at times.  I have found that they are a lot harder to take off than put on, especially if you're doing it by yourself, so I make an extra effort to place them properly the first time.
 
Here is a size chart for bands:
• 4: Baby Chicks, Quail, Small Pigeons (1/4")
• 5: Medium Pigeons, Pheasant Hens (5/8")
• 6: Large Pigeons, Homers, Month Old Chicks, Pheasant Cocks (3/8")
• 7: Bantams, Half Grown Chicks, Ring Necks, Mallards, Wild Ducks, Hamburgs (7/16")
• 8: Call Ducks, Water Fowl (1/2")
• 9: Large Leghorn Hens, Wild Ducks, Ancona Hens, Campine Hens (9/16")
• 10: Chickens, Pheasants, Ring Neck Cocks, Wild Turkeys (5/8")
• 11: Plymouth Rocks, R.I. Red Hens, Wyandotte Hens, Leghorn Cocks (11/16")
• 12: Jersey Giant Cocks, Turkey Hens, American Breed Cocks, Geese (3/4")
• 14: Turkey Hens, Geese, Swan, Cornish Game (7/8")
• 16: Turkey Toms & Geese (1")