High levels of cheesiness...
Both shinta and Dark Dragon's suggestions are good, Kenichi, Shaman King, and Law of Ueki are all right up there, so is GTO and Ranma 1/2.
Not going too deep into mecha, Vandread may be a good choice. Space, men and women separated for centuries, each thinking the opposite sex are 'aliens.'
Outlaw Star is always a series that reminds me of Trigun to some level or another. Another space series, but with ships that fight hand to hand, so there's just a little mecha involved too.
If you really liked Trigun, there is a good chance you will really like Gun x Sword. I didn't watch a lot of it, but it is the same post-apocalyptic, gun shooting kind of thing, and yes, there are even mechas.
Another you might like on the same lines is Coyote Ragtime Show. One master thief and crew and one orphaned girl with two interstellar police officers out to catpure him and 12 sociopathic andriod girls out to kill them.
Nurse Witch Komugi-chan is intentionally weird and cheesy. A strange magical girl spin on becoming an idol. Emphasis on strange. Pretty much straight up comedy since they never take it seriously.
Kaleido Star can be kind of cheesy. Details the rising stardom of Sora, a girl from Japan who moves to America to join the Kaleido Stage, a theatrical/acrobatic troupe similar to Cirque de Solei.
Hyper Police also had a certain cheesiness to it. It takes a world where there has been some sort of apocalypse, and now humans are far outnumbered by monster-people when the two worlds were combined. It follows a small team of bounty hunters (catgirl, werewolves, kitsune, etc) outsourced by the police to deal with issues that arise.
Dominion Tank Police: Whole new level of cheese. This an OVA, 4 episodes. an officer, Leona is transferred in from the motorcycle-division, and has a little problem getting used to the tanks (she crashes them, a lot), and destroys the personal tank of the units commander, Lt. Britain. She cobbles together a new tank out of what's left, and it barely exceeds the size of a SMART car. There's some plot about evil catgirls wanting to steal certain bodily fluids for some nefarious purpose, but I saw it years ago, and to be honest, really wasn't paying attention.
Ikkitousen (the whole franchise). It's all panty shots and martial arts. which brings me to...
Najica Blitz Tactics. Same thing, but replace martial arts with guns. This is the series whos box set infamously came with a pair of panties...so you can see where it is going (and no, I do not own it).
Busou Renkin Shonen series not unlike Bleach, who wrote in a considerable level of cheesiness into the storyline.
I'd suggest Team Medical Dragon, but it is only a manga and a live-action drama (that I've heard it quite good actually).
If you want cheesy romance series, that is a whole different list.