Designated Girl Fight: With Ankh Su-Namun in the first two films. Justified in both. In the first, Ankh Su-Namun needs to kill Evey to become immortal (and then the guards summoned by Jonathan have no qualms about attacking her). In the second, Evey has fought her before in their past lives so she's the best qualified to take her out. Jonathan tries to fight her but backs off after one punch.
Let's Get Dangerous: Jonathan may be a ridiculously greedy, swindling Plucky Comic Relief, but he is also a crack shot with a rifle, a skilled pickpocket, and disturbingly competent with a book of ancient spells.
The first moment he really seems to Get Dangerous is the climax of the first film: when the first reanimated mummies appear in the treasure room and his two-shot derringer proves almost useless, he promptly pulls the revolvers from Rick's holsters to continue shooting.
Chekhov's Skill: Like his uncle Jonathan, Alex is established early on as learning how to read hieroglyphics. This eventually pops up after Evy dies and they need to resurrect her using the Book of the Dead... written in hieroglyphics.
Idiot Ball: As Rick lampshades, what the hell was Alex thinking when he decided to go and uncover the Emperor?! It's not like his family haven't had a long history dealing with curses and mummies... does it ever end well?!
May-December Romance: With Lin. Although Lin is about the same age as Alex, she and her mother had been rendered immortal for 2,000 years due to the power of Shangri-La's waters. Of course, her mother took care of the problem by sacrificing their immortality in order to summon an undead army to stop the Emperor.
Nice Job Breaking It, Hero: He inadvertently awakens the Dragon Emperor from his tomb simply by digging him up. Of course, he was being manipulated into doing so at the time, so it's a given.
The Smart Guy: He is intelligent far beyond his years, a trait his parents never hesitate to acknowledge. He is able to speak and read Ancient Egyptian better than Jonathan having been taught by Evelyn and is able to use the Book of the Dead to resurrect her when she is killed by Anck-su-namun.
Too Dumb to Live: Alex in the second film. Given who his parents are, all of the ancient traps and cursed objects they've encountered and that the Temple they found the Bracelet in immediately self-destructed upon its removal... what made him think that putting the damn thing on his arm was at all safe?!
In fairness, he was Nine at the time.
This doesn't however forgive his stupidity for waking up the Emperor in the third film.
Cruel and Unusual Death: Having abandoned Imhotep in favor of her own life, she stumbles and falls into a swarm of scorpions (and possibly the flesh-eating scarab beetles) as she is fleeing. The scorpions/beetles crawl all over and inside her, choking her dying screams.
Cute Monster Girl: Subverted in case of her mummy form. She looks exactly as you'd expect a 3000-year-old mummified corpse to look.
Being Evil Sucks: Beni sums up his lot in life very accurately: "I need a new job."
Cruel and Unusual Death: Having spent the movie betraying everyone, he faces a slow death by dehydration and starvation after being trapped in Hamunaptra's treasure chamber. That's bad enough, especially given that the single torch he has is going out. Cue those flesh-eating scarab beetles.