L.W.
One year old parties are tricky because you are usually working around a nap schedule and the guests may not be on the same schedule. That said, I don't remember trying to throw one for any except our first child. We invited grandparents and godparents and a few neighbor kids. Then she got pink eye and we cancelled...so we threw a "half" birthday six months later and it was very fun.
We had lots of balloons and let the little ones hit them around, and plenty of food for adults and kiddos. Bubbles are always a hit at this age.
Another caution: I was going to be strict about no sugar until age two (my children though a donut was a bagel :) I used a cake recipe that had only apple juice concentrate to sweeten it and it turned out to be a brick. We bought a real cake for the 1/2 birthday :)
Another party idea for 1 yr. olds. Scarfs they can toss as they listen to music, and music making instruments like jingle bells and egg shakers are fun.
Update: We didn't let the kids try to blow the balloons up, and if one broke we collected all pieces and threw them out right away...my one year old is now 14 and somehow the other six children managed to survive balloons, too. It is always good to be cautious and attentive whatever the activity. That said, my neighbor's son is very allergic to latex so one must watch for that.
Another idea: perhaps the adults could join the children in a game of pin (using tape not pins) the tail on the donkey (or some variation depending on your theme...if you have one...I've seen stick the dots on the lady bug and so on) I remember my dad playing this on his 40th the adults had a lot of fun with it. A few years back Martha Stewart had some lovely ideas for one year old parties, maybe they are archived with Martha Stewart Living Magazine's website. Also a great source is www.familyfun.com