Ladies often take after their fathers, and even if they don't, this belief is so common that you can easily riff on it during your groom's wedding speech. Drawing a link between the bride and her dad will instantly endear you to the audience, as this inoffensive source of humour also invokes the feeling of family within the room.
One of the most potent topics you can tap is the father's profession; by drawing a line between this and your bride's traits or personality, you'll create a more visceral type of humour than clever wordplay or observations alone. Take this first line, for example, which uses the father of the bride's job as a starting point to make a general comment about the bride:
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"Our relationship started out quite tempestuously, as Karen played extremely hard to get for the first few months. She really gave my heart a wrench, which now comes as no surprise, being the daughter of a plumber."
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"I feel like I've become a bit of a social climber since I met Eliza. I've met so many new and exciting people. I guess that comes with the territory when you date an electrician's daughter; she's got all the right connections."
As we've just demonstrated, the link between the father's job and the bride does not have to be literal. If the bride is genuinely good at fixing taps because her dad is a plumber then fair enough, but for most people this won't be the case, so you must use creativity to link the two things by deploying puns, double-entendres or metaphors:
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"Anyone who has met Gina knows she's incredibly kind and generous, and this extends to conversation too. She will always let you have your say and respect your opinion, but this is a trait she has not passed on to her daughter Elizabeth. No, Liz takes more after her father Rick, an architect, as every time we argue she's the one with all the angles."
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"Amanda really does keep me in check, as being from a religious family she holds me to a higher standard than my friends do. Even if I wanted to, I couldn't lie to this girl. She's the daughter of a minister. I can't get anything pastor."
Self-deprecation can be worked into this kind of joke too, as you can make fun of yourself while also complimenting your wife through references to her father's chosen profession, as this next example shows:
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"Helena's father Pete is an actuary, but I fear his skills may have not passed on to his daughter given she's chosen to marry me. There's no way she's calculated the risks, I'm sure she's unaware of her true value, and if you were to describe me in terms a statistician would understand, the most commonly used words would be 'mean and average'."
This style of humour works well as a standalone joke, but it could also serve as a way of introducing a topic for which you have no natural opening. For example, you may wish to move from how you first met the bride to a quick mention of her parents, and the following joke would help you do just that:
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"I don't want to go into too many details regarding mine and Rachel's first date, but I will say that she certainly made me wait for any kind of intimate affection. Her father Derek is a barrister, you see, so she's been raised to keep a tight hold on her briefs."
Another segue you may need help with is the articulation of your thoughts on the future of your relationship after discussing something else. Let's say you've just been talking about the parents and how you first met them. You'll probably have mentioned the dad's profession already, so there's no need to set it up to make any further jokes work. Next, it would feel natural if you implied you'd like your own relationship to follow their example, and you can drop in a nice little call-back to the father's job while you do it:
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"I really do respect Jan and Jack for keeping the love alive for 30 years now. Round of applause for that please! [Pause] I hope that Francene and I will enjoy as happy a marriage as you have. I'm genuinely optimistic for our future, you know. Not because of my own personal feelings, but because Fran has her father's ability to forecast stormy times ahead, and she's given us the all clear for years to come. I must trust her judgement. After all, do you see it raining outside?"
Of course, not every girl grows up to be like her daddy. Sometimes your bride's traits will be the exact opposite of those implied by her father's industry, but this is just as solid a basis for observational comedy as any:
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"Children have a habit of rebelling against their parents, and I see a lot of that in my new wife Tricia. Her father Barry was a coal miner - as rough and ready as you could get. She's the opposite, an absolute glamour queen. Tricia must've seen him come home night after night with muck on his nails, stuff in his hair and a face caked in god knows what. Whereas with Tricia, she comes in from the club with her nails painted, hair stuck up with all sorts and her face caked in… you know what, they're not too different after all."
Finally, let's tackle the potentially morbid topic of a sadly absent father. If the dad is alive but not attending then this is something to avoid, but if the bride's dad has passed away and it seems appropriate to mention him, you'll bring a tear to the eye of even the most hardened soul if you invoke his memory on his daughter's big day:
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"Sadly, I wasn't lucky enough to meet Laurence while he was alive, but everything I hear about him makes so much sense when I think about my new wife Kelly. He was feisty, and so is she. He was fair, and so is she. But the most impressive thing I've heard about him was how he worked tirelessly his whole life for the betterment of others. As the head of a local charity, he transformed his community and didn't care that the wage was half that of his old banker's salary. He knew the value of happiness, and so does Tricia. He knew what was important in life, and so does she. He was generous, and she married me!"