I know this is gonna make some people angry, but I don't find Family Guy amusing at all.
I agree where you're coming from. I used to love Family Guy, but when the fourth season appeared, I stopped watching it. Not necessarily because it was random, but because the jokes were becoming too commonplace, too long, and too degrading.
Too Commonplace: Despite the random nature of the jokes, it's easy to see that patterns have shown up, making it as though you're watching the same thing every time. Several times there has been a joke in which one person walks in on another doing something embarrassing, and just stands there saying "Oh...hi... I see you're [doing this]... I'll be going now." Or another in which (pop-culture) characters are doing their normal routine, stop and start bickering and complaining about their lifestyles. There has also been an increase in "Let's crack on Meg Griffin" jokes (Seth MacFarlane states "It's hard to get in a teen girl's head"), which were scarce in earlier seasons and demonstrates the laziness to develop Meg's character or that she is used as an easy joke out if no others can be thought of.
Too Long: Worse than a random, nonsensical joke that doesn't make you laugh is one that goes on for two minutes. A whole tenth of the episode's airtime. An example is when Osama Bin Laden is trying to film a new threat video but keeps screwing up. It was funny for 20 seconds but it quickly lost momentum.
Too degrading: The bulk of Family Guy is shock value, so vulgarity is prominent. In earlier seasons, it was subtle enough to laugh at. Now it's characters cursing at every chance they get (even Lois about her own husband and children), flatulence and bodily fluids spewed everywhere, more violence, more political criticism, and more sexual related jokes. It's almost as if Family Guy is trying to be on the same level of South Park humor, but is failing to see the importance of balance between vulgarity and context. With its political jokes, Family Guy is too one-sided ("wah, we have to go to a Red State, where they're all morons" or "don't give me that Republican crap"). While that I don't have a political standpoint, this shows that Family Guy chooses to lampoon only issues and people in ways that won't offend their target audience. South Park manages to lampoon all sides of a political issue, which I do find to be a good balance. As a side note, Family Guy never really focused on politics to begin with, so it seems (at least to me) out of place with its formula.
