The amount of exercise varies per individual hamster (also the species) but on average in the wild, they run between 4-7 kilometers a night if that gives you a rough idea.
I'd handle it as much as you want, just make sure if it starts to appear stressed - give it a break and end playtime.
Hamsters can get depressed, but some of that isn't just because of owner attention - it's from shear boredom. Here are some ways to both interact with your hamster, and keep it entertained and happy :)
The best way to keep your hamster from getting bored is to change things up in their cage once a week. Not their house, food, water - but their toys and treats.
Be aware that sugary treats and all fruits should be avoided with dwarf hamsters as they're prone to diabetes. They can be given in moderation to Syrian (Teddy Bear, Honey Bear, Golden, Panda) hamsters - but still don't go overboard with them as it can still affect their teeth - remember, they can't brush their teeth!
Hamsters get bored very very easily. A giant box full of different toys,a bowl of chinchilla bath sand (not dust!), a maze made out of paper towel and TP tubes are all fabulous ideas. You can get a really big plastic bin at any big store like Walmart or Target for under $10. A big thick cardboard box with even more walls and doorways made of cardboard can be even better because it's free - just be sure you check it before you place the hamster in each time for any holes or signs of potential holes :)
Place your hamster in his or her "play zone" whenever you want to play with it. Hide treats in the tubes so they can be discovered. You can make homemade wooden toys out of interlocking craft sticks that look like popsicle sticks - and they're great for their teeth as well.
Hamsters love to run around in an empty bath tub as well! Put the plug in, or cover the drain with a piece of cardboard so paws don't get trapped and never leave them unattended.
With chinchilla bath sand - not the dust as they can breathe it in too easily - you'll want to place the packet of sand in the bowl. Place the bowl either into their new play area, a larger bowl, or on top of some newspaper or toweling. They will roll flip and dig in it so you'll want something under it to catch any mess and make cleanup easier.
An idea from Stubby McMini and her hamster (I give credit where credit is due - and this is a fabulous idea!):
"...he also has a homemade 'maze' that he adores.... I got a big cardboard box and put in 'walls' theres a room with soft bedding and treats hidden, some steps, a couple of arch doorways, toilet roll tunnels, a bish bash room.... he loves it, though he does try to climb over the side so you have to watch him carefully!"
I love her idea! She's also very very correct about never leaving your hamster unattended no matter where it is when it's outside its cage, including when they're in their balls!
Speaking of their little roll-a-thon balls. Make sure that you have an appropriate sized ball for your hamster! Syrians need the larger balls, dwarfs *must* have the smaller ones or it can cause serious back problems for either one. Color makes no difference to a hamster as they're color blind, but the clear ones will make it a lot easier on them to look through as far as getting around because they don't have really good vision to start with. Not as cute for us to watch, but easier on your hamster!
Good luck - please feel free to msg me if you need any additional advice :)
13 years of hamster rescue, rehab and owner education :)