Reaper rounds increase the damage of conventional weapons (by increasing the crit chance by 20%), but double the weapon's range penalty. It's your choice of whether to use them or not according to your play style and preferred tactics.
Take notice that they only affect conventional weapons so once you move all your squad to laser/plasma weapons, the Reaper Rounds will have no effect.
Here are two notes about their usage from Xcom wikia:
Reaper Rounds are an effective way to increase the potency of conventional weapons before better items, such as Beam Weapons are researched and manufactured. The added technological and research options in XCOM: Enemy Within can delay a player's progression up the basic weapon research tree significantly, especially at Classic or Impossible difficulty. Reaper Rounds can help give a damage output boost to classes such as the Assault, Heavy and Sniper, the enhanced weapons for whom must be researched separately, incurring greater costs in money and time compared to upgrading the base Assault Rifle quickly.
Reaper Rounds shine when given to Shotgun build Assaults, given that their weaponry specialization largely negates the range penalty, and increases crit rates that such troops are often reliant on to clear an enemy. Reaper Rounds also work well when given to Snipers, as the range penalty on Sniper Rifles is for close-range attacks versus long-range. Heavies benefit less from Reaper Rounds, since their lower base Aim reduces the number of crits that actually hit, though if a player adopts a strategy of Heavies closing with enemies more this deficiency can be compensated for. Supports and Rookies benefit the least from the use of Reaper Rounds since the range versatility of their assault rifles is negatively impacted.
As to my own experience, I didn't use them because I prefered to have the scope to increase aim instead of them, and I researched laser weapons before I got tactical rigging, so it wasn't relevant any more. I did research the tech needed for tactical rigging before the laser weapons, but didn't have money for the foundry project, and didn't see it as important enough.
At the start of a game I usually have very little funds and can't afford a lot of things so I try to get only the absolute necessity. At the start, the soldiers are poor shots anyway and the enemies have relatively low health, so a penalty to aim in my mind is much worst that an addition to damage.
On second thought, they might be good to take on the first terror missions to deal with the problematic chrysalids, they don't take cover, so hit percentages are usually high, but they have a lot of health and a 1-hit kill attack, so killing them quickly from close range is a priority, although I didn't try it for myself.