I have 2 DS - aged 7 & 4 - to set my answers in context...
Does your child have a set limit on gadget time a day / a week? Why is this? How long? Does this work for you and them?
Nothing set out - although depending on the time of day and what other plans we have depends on how long they are able to play on something. On a wet holiday day with few plans they would be able to play on the Wii for longer than they could on a school day for example. I do try to tell them at the start if time is going to be limited and then give warnings in the run up to 'time to stop playing - NOW' so it doesn't come as a surprise which works well.
DS2 has a mobigo which he adores and will quite happily sit down and play for hours sometimes if nobody stops him. They also share a storio and leapfrog explorer and both boys will happily play on these on car journeys or at home. DS1 in particular I try to encourage to play on some games as they are for spelling which he is particularly bad at. Others include maths games which he loves because he loves maths and that's good too - I'm happy that he associates learning with fun and games, and being enjoyable.
Sometimes some of the biggest problems come about when there are two children who both want to play on the same gadget at the same time - kitchen timer comes out and they get 5/10 minutes each and then a strictly enforced handover, regardless of whether they are about to get their highest score (otherwise ds1 has been known to take another 10 minutes just to 'finish' his game... ).
Both boys also love playing on the iPad and iPhone - they know this is a treat as they are mummy's toys and she's not very good at sharing so promise of a few minutes play on the iPad can be a good bribe reward or distraction if one of them hurts themselves.
What tips would you share with other parents about how to handle gadget use with children? How do you generally view use of these gadgets? What do you think are the benefits - to parents and to children? And what do you think are the disadvantages? (to parents and children)
The children have to know they have to respect the gadgets - they are expensive and easily broken - and the fact that they don't automatically get to play on them as and when they want.
They are a useful bribery/reward tool and they can be educational - it's good to ensure that there is a mix of games so that they do play stuff that is educational as well as pure fun, because it helps to reinforce the fact that learning is not just boring stuffy classroom stuff as it was in my day [sad old gimmer smiley]
I also think it is important they are exposed to a range of technology from an early age - in this day and age so much of life interfaces with technology at so many different junctures that the more exposure to different ways of interacting with it they have, the easier it is going to be for them going through life, whether it's discussing the latest game in the playground or puzzling out how to learn to use a new piece of software or product, or even going on to design or programme new software/hardware/products in the future.
It also helps them to learn how to concentrate on something - useful at school and beyond!
disadvantages - children can become over-dependent on them or addicted to them to the exclusion of other activities - but it's up to the parent to stop this.
If your child doesn't use a gadget like this please say why - it is down to you or them?
DS1 doesn't have a DS yet despite wanting one - down to me and dh as we think he has plenty of access to gadgets to play with and we're not convinced he would look after it particularly well - he still loses lots of his things. however I have no problem with him playing on them - if we are at his cousin's house or at a friend's house for example. it's also partly because we can't afford to buy everything going - so we have a Wii and an iPad, his friend has x-box and a ds etc etc. They enjoy playing on them at each other's houses but doesn't mean that they get to have them 'just because'.
The other good thing about this is that ds if he doesn't have something will make it for himself - so he has lots of paper ds, iPhones, iPads, etc that he has made, all drawn out and then he'll draw a game on the screen and pretend play with it. which is great - both because I love watching his inventiveness (this goes for everything, not just gadgets - he also has a complete steve backshall paper animal filming / hunting kit including snake hook and abseil rope he's made for re-enacting that out, his own set of moshi monsters and pokemon that he has designed etc). And because - although he doesn't yet know it - he's actually discovered how to design, create, modify and improve lo-fi paper mock ups which is a great skill should he ever get involved in web design (amongst other things) when he is older (and is something that both dh and I do as part of our regular jobs!)
What sort of games or apps does your child play with? Do they play with other children? If so, do they socialise when on it?
All sorts of things - wii favourites are Mario kart, Phineas and Ferb and the Sports Resorts games but will happily play lots of things.
iPad/iPhone - I have loads of games on there but both boys will dip in and out of everything. ds1 loves lots of sports games, puzzles, mazes, spiderman/hero games but also maths, phonics and alphabet stuff.
DS2's favourites include Dora, colouring games, all the maths, phonics and alphabet games, listening to stories and some fab simple duplo ones. He started using iPad/iPhone at 2 and despite not being able to read he can happily whizz around on them, find the games he wants, get them started, understand them and figure it all out.
Rarely socialise on gadgets - just playing at home with each other or if a friend comes to play and they are all on the wii. they will watch each other playing on iPad/mobigo/etc sometimes. They don't have any games that are linked to other people remotely and I quite happy about that!
Does the game ever become reality? For example - do they act out the game in real life? Do they/ you integrate the game characters into other activities eg making an Angry Birds cake or playing Skylanders in the park?
Only become reality when ds1 makes his own paper prototypes to play with for when he can't play with the real things. He might play at sonic or mario with friends or end up doing kung fu things that he's seen on games but these days so many things are multi-channel that he'll of seen things on tv or in comics or on websites as well as on gadgets so it's difficult to know where the main influence is coming from or if it is the sum of all the different things.
ds2 can get a bit over exhuberant if he's been watching his brother playing on the wii (ds1 has somehow convinced ds2 that 'they' are playing if ds1 is actually playing but says things like 'look we are winning' or 'we did a great shot there' while ds2 sits and watches 
) and doesn't realise that if he's attacking someone as he has seen happen on the game that actually one or both of them might get hurt, but he's beginning to realise that and it's calming down, hopefully will soon be gone.