The conventional wisdom is to invite as many guests as the age of your child: turning 6 yrs. old? Six guests come, not counting the other crumb-snatchers at home (who are the designated official "helpers" for the day, at whatever level they are capable.) This is a wise choice. Three year olds can be great helpers!
Other than that, i am appalled at the trend these days to make each party bigger and better than the last one, than the neighbors', than the cool kids' at school, etc. If we have pony rides when they are 4, what will be done for an encore when they turn 7?
Keep in mind: Kids do not retain specific memories of most things before about age 7. When s/he does "remember", most usually they are remembering the family stories and photos of the event. Exceptions: a trauma (such as car accident, abuse, the house burned down, hospitalization) or sometimes a particularly impactful event.
However, they DO retain the feelings / impressions of events. Going to Disney: they'll remember it was a good time, or meeting Mickey (which will likely scare them, depending on personality!) ... but the younger they are, the less they remember.
So, back to parties: even in this technologically sophisticated world, most kids still like interactive events during which they can spend time with a parent (or at least an adult or the older kid helper hired for the occasion), too.
Crafts, simple games, helping to make the goodies (such as slapping together the cheese and tomato sandwiches for frying; using cookie cutters to cut out the cookies for baking; helping to mix the bubble solution for the bubble blowers; helping to color the home-made playdough) ... all these are fun, adjusted to the child's age. Yup, this takes more effort on mom's part, but the memory-making is worth it.
The general guide is to have some sort of activity as you wait for everyone to arrive; then do something very energetic; then something quieter, then gifts, then the thank-you to Jesus prayer, and food. Then home!!! Longer is not better. Keep a trash bag handy for the discarded wrapping paper. Your official helper writes down who gave what (for the thank you notes.)
The caveat is that this works less well as they grow older, and are influenced by school mates. Twelve-year olds aren't so easily impressed, and are much more conscious of being cool or not being cool. It takes a good bit more creativity then. But even then, kids deep down crave interaction with a caring adult more than a magic show, or being given $5 worth of tokens for the video game room. This is also a good witness to kids from homes in which they don't get such attention.
I read a very interesting suggestion: that the moms of a group of friends or classmates meet to discuss, and band together, to avoid one-upsmanship. Can't hurt to try! Obviously this works better if you actually know those moms, but what a good reason to get to know them (to band together for the good of the kids!)
Don't be so involved in taking pictures or video that you are not "with" the kids. Have someone else do that.
Preparing for the expected deviations is a good thing, too. Keep a throw-up bowl and towels to wipe spills very handy. Get down at kid level to observe safety dangers. YOUR kids may be well-trained in not touching mom's prized African violets, but other kids may not be so disciplined. Emotional breakdowns or fights? -- not uncommon on such a high emotion day. Plan for a distracting activity. Keep first-aid materials very handy. When a kid falls and cuts his knee is not the time to go hunting for a bandaid.
Also, many times, I was shocked to see visiting kids opening cabinet or closet doors, or wandering down the hall to open bedroom doors, without permission, even when mom was sitting right there! Be aware that this can happen. That's why it's helpful to have at least one other adult or teen helper for supervision. (Needless to say, you teach your offspring to not do this at someone else's home!)
Your kid needs to say good-bye and "thank you for coming" to each kid when they are leaving, if possible. This teaches the manners of a good host (putting others first.) Have your child also help clean up a tad, even if it's in the most rudimentary way,
Finally, teach and role-play with your kiddo to say thank you (loudly) for the gift s/he is opening. Teach her that even if she already has this item, or just doesn't like it, she can still be thankful that the other kid was generous in giving it to her. Also, thank you notes are a good habit to start at an early age. When the child is very young, you can write the note and just have them print their name (if they can). Some like to draw a picture of the gift, and you can just write the "Thank you" on the paper. Even the littlest can lick or place the stamp on the envelope.
I didn't allow my kids to get the cash from the checks from grandparents till the thank you note was written and mailed! In the note, they were required to say what they might use the money for (a game, saving towards such and such, etc.)