How can I counter enemies with Riot Shields in Mass Effect 3
Pull - Grabs the shield out of an enemy's hands, leaving them exposed.
Stasis Bubble - Stasis Bubble (level 6 stasis upgrade) will cause an enemy to drop their shield. Sometimes they seem to block the initial hit, but as soon as they move at all, they get caught in the bubble trap and the shield falls.
Armor Piercing Ammo / Piercing Mods / Widow, Black Widow, and Javelin Sniper Rifles - Ammo, mods, and weapons that provide an armor-piercing capability allow you to fire THROUGH a riot shield (and other light cover). The M-98 Widow, Black Widow, and Javelin sniper rifles have armor-piercing rounds by default (no ammo or mods necessary). In multiplayer, armor-piercing rounds can be purchased at the store and equipped on the "Equipment" screen.
Well-Aimed Headshots - The Cerberus Guardian's riot shield has a view slit right at head level, and you can shoot through the slit and score headshots if you've got good aim and an accurate weapon. The "Mail Slot" achievement/trophy is awarded for killing 10 guardians in this fashion.
Singularity - If you aim above or to the side of an enemy holding a shield, sometimes you can get a singularity to "curve" and hit the enemy from the side or behind, avoiding their shield. The enemy will drop their shield if they are caught in the singularity. It's a little tricky, and doesn't work in all situations, but with some practice it can be effective.
Forceful Attacks - Many special powers will cause an enemy with a shield to stumble and lower the shield temporarily, giving you a window of opportunity to shoot them while their shield isn't blocking them. Includes, but is not limited to: Throw, Shockwave, Charge, Nova, Concussive Shot, etc...
Flank / Combat Drone - If you and a teammate can flank a enemy with a shield, one of you should have a clear shot - The shield only faces one direction. In the absence of a teammate, a Combat Drone can be deployed behind or to the side of the enemy to attract their attention.
I've found two good ways to handle the Riot Shield enemies.
The first is the "Pull" power. For lack of a better term, Pull on Cerberus Guardians (or any other enemy with Combat Shields) is "Super Effective". It will strip the shield away from them, making them just as vulnerable as any other average enemy.
The second method is easiest to pull off with a sniper rifle.
The riot shield only has a single weakpoint from the front -- there's an unarmored view slot at the top of the shield, at head-level.
Simply thread the needle with your bullets, and they'll fall just as quickly to headshots as any other enemy.
As said above, the 'Pull' power yanks the shield away if you have it.
A little coordination goes a loong way. Their shields can only face one direction at a time; have a teammate distract them while you flank around them.
If you choose your targets carefully, you can Vanguard Charge into the guy behind the one holding the shield, then turn around fast to maul the Guardian before he can turn to face you.
The Shockwave power (Human adepts get it among others) knocks them off balance for a few seconds. Follow it up with heavy pistol shots, or have your teammates ready with a sniper rifle to take advantage.
A little careful aim can let you drop a singularity behind them, where they'll be picked up and tossed around as usual.
I could go on, but the bottom line is that the only attack method that isn't highly effective is a guns-blazing frontal attack. Anything else works just fine.
If you're having trouble in the early Mars mission with the Cerberus troops, you're supposed to be using Liara T'Soni's Singularity skill (that's the blue alien girl). Singularity picks up the soldiers and forces them to drop their shields. Open the Skill menu in combat, aim toward the troops with shields (you can do this while the menu is open + time is paused) and select Liara's Singularity skill. Boom, no more shields.
That's why she has it, so no matter what your character is, you can disable the shield-carrying enemies on Mars. Otherwise you can use the various skills mentioned in other answers, but your character might not have them.