A full list, like you most likely had to know in general chemistry?...most likely not. However, you should commit an abbreviated list into memory.
1) ALL Group I metals, Ammonium salts (NH4+), Nitrate salts (NO3-), Perchlorate salts (ClO2-), and Acetate salts (C2H3O2-) are soluble
2) MOST Lead 2+, Silver, and Mercury I salts are insoluble.
Way to try and Blue Falcon a fellow SDNer. j/k, I'll assume that was an honest mistake.
OP, yes you should probably have an idea of what is almost always soluble like the above poster mentioned. I think it is also worth noticing that *usually* the conjugate acids/bases of strong acids/bases are soluble in all instances. (NaOH/Na+ always soluble, HClO4/ClO4- always soluble, etc.).