It depends on what is in the marinade. If it is chicken and I plan to grill it, I just take it out of the marinade and put it on the hot grill.
If it is tuna, I usually use paper towels to get most of the marinade off before cooking.
Marinated shrimp usually go right to the grill.
Swordfish also gets wiped with paper towels before going on grill (with mayonaisse spread all over the swordfish).
Hope this helps.
Ray