well, i dont really have any fave episodes...i have a whole whole lot of fave episodes. several in each season.
for the original csi, (all in no particular order) in the first season (i haven't seen them all yet), table stakes, strip strangular, justice is served (the first one i've ever seen...although i didn't realise it was csi at that point), cool change, and boom. in the second season, identity crisis, primum non nocere, felonius monk, scuba doobie doo, stalker, cross-jurisdictions. in the third season, a little murder, play with fire, crash and burn, got murder, precious metal, execution of catherine willows, and the accused is entitled. in the forth season, assume nothing/all for our country (i know one of the guest actors...), feeling the heat, butterflied, turn of the screws, xx, grissom vs the volcano, 11 angry jurors, and invisible evidence. in the fifth season, down the drain, who shot sherlock, mea culpa, grave danger, 4x4, snakes, and ch ch changes.
for csi miami, in the first season, golden parachute, just one kiss, spring break, camp fear, double cap, breathless, and tinder box. second season, hurricane anthony, not landing, mia/nyc non stop, extreme, grand prix, and witness to murder. i've only seen the first 4 eps of the third season because it comes late where i am, but of those four, i like lost son the best.
for csi new york, i've nearly finished the whole season, just the last 2 hasnt been shown yet. of those ive seen, i like american dreamers, rain, 3 generations are enough, night mother, till death do we part, and dove commission the best.
about fave characters, well, i dont really have any because i dont pay so much attention to them, just the cases and that sort of stuff. i watch csi because of the cases, the forensic evidence, knowledge, etc... although for csi new york, i do have a fav character - mac that's only because i've seen gary sinise in several other movies previously.