Here are a few ideas for games:
Coin in glass game: in this game, a glass with a small diameter (approximately 1 1/2 to 2 inches wide) is placed on the floor with a starting line marked at approximately 3-4 yards away. The participants form a line behind the line, and one person goes at a time. The person who's having a turn is given a quarter, and s/he places the quarter between her thighs. The purpose of the game is to not drop the coin and insert it into the glass; they cannot use their hands in the game. The person who inserts the coin wins the game. If there are more than one person who inserted the coin, there needs to be a tie breaker after everybody had a turn. The winner gets a prize.
Draw the baby: There is also another game where you give each participant a piece of blank paper and a pencil. They have to place the paper on top of their head, and draw as best as they can, a baby. They cannot see the paper. There is a time limit (approximately 4-5 minutes), and the winner is the person who draws the picture that looks most like a baby.
Pins on a hanger: here a person goes around with hangers that have many cloth pins hanging on the wire. This person goes around the room and asks each participants to grab as many pins as they can in one hand without dropping any. Once a person drops a cloth pin, s/he is out and his/her number is the amount of cloth pins that s/he had in his/her hand before s/he dropped the pin. The winner is the person who has the most pins. If there is a tie, you can either give each person a prize, or you can have a tie breaker.
Optional: as the person is grabbing each pin, s/he has to name a baby item.
Mistery box: In this game, you put a lot of different items related to babies. The box has a hole for people to put their hand inside the box. One person goes around the room and has each participant put their hand inside the box and feel what it is inside the box. They have one minute to feel the contents. After their time is up, they can start writing down what items they think the box contains. You can put items such as diapers, pins, the horns of the breast pumping machine, socks, pacifiers, birth announcements, etc.. After everybody has had a turn, the contents of the box are revealed, and the participants count the number of items that they got correct. The winner is the person with the greatest number of correct items.
Diaper wrapping: This game is played in couples. Each couple is give a roll of toilet paper. One person is going to be the baby and the other person the caretaker. The caretaker has to diaper the baby with the toilet paper. The couples are given a time limit (perhaps 10 minutes), and the winner is the couple who was the most creative and/or the neatest. You can choose whichever category you want, but make sure to tell them in advance.
What's in the diaper?: You can smudge some melted chocolate or another food item on a diaper, and you blindfold a person or two. The person can feel and taste the diaper, and then at the end states what they think the diaper contains.
Who am I?: Each person gets a sticker on their back with the name of a baby-related item. The participants are paired up, and his/her partner has to give them clues as to what they are. The person guessing can only ask, "Am I a ...?", and the partner says yes or no. Once the first partner guesses, s/he helps his/her partner figure out what s/he is. The couple who guesses first wins.
Baby bank: this is the baby's first piggy bank. You give a specific amount (let's say 25 cents), and give one category, e.g. the most memorable moment in your childhood, an anecdote in your childhood, your most embarrassing moment, your first crash, the worst lie you've ever said, a joke, which animal represents you and why, etc. You can also have some commands, such as, jump in one leg, act as a monkey, play a chicken, roar as a lion, give ten turns, dance the hokey-pokey, sing "I'm a little teapot", cry like a baby, etc. As each person participates, s/he places the quarter in the piggy bank and answers the question being asked. You go around the room and each person gets a chance to answer each question and place a quarter as they are answering the question. You can give people the chance to not answer the question, but they would have to put in 50 cents instead of 25. You can play as long as you want to and have as many questions as you wish, you might want to consider the number of participants.
Baby bingo: here you can create bingo cards with baby-related items or you can give each participant of piece of blank paper, and direct them to make a 4 x 4 or 5 x 5 card. After that, tell them which items they can put int he boxes. You can have a couple of extra items if you wish. They you just start calling out the items, and the persons who have four in a row, four corners, four in the middle or blackout win. You can also have letters as category or last person standing.
Uscramble: You can have a few baby-related words scrambled on either handouts for each participant, given them a time limit to try to unscramble them, have them exchange papers when time is up, and then go over the answers. The person who has the greatest amount of correct answers wins. Variation: Instead of having the words on handouts, you can play with the whole group by writing one word at a time on a whiteboard. You can split the whole group into smaller groups. After you finish writing the word, the groups discuss what the word is, after a half of minute or a minute, each group has to send a representative up and the representative who writes the unscrambled word correctly the fastest earns a point for his/her team. The team with the most points wins.
Dress-up race: Two people go to the front at a time. There are a lot of clothing items on the competing area. You give them a time limit (3-5 minutes) and they have to start putting on the clothes on the area as fast as they can. The person who puts on the most items on wins. For this game, make sure to not use clothes that you would regret being ripped because they could.
Obstacle course: You can have different challenges in different areas for two teams. Challenges could include changing a diaper in a doll, carrying your partner from one point to another as a baby, changing a doll's clothes, wheelbarrow, making five or ten water balloons and carrying them from point A to point B in a bowl jumping on one leg (if they drop a balloon, they have to go back and make another one), on point B break the balloons by either sitting on them or breaking them with their teeth (you can also have them break them in partners; the partners break them with their teeth, or they can break them by throwing it at each other), at the end of the course, you can have them toss pennies into a bottle and advance until they insert a penny. The winning team is the team that completes each obstacle successfully and reaches the finish line first.
Don't cross me: this is the traditional game where each person gets a baby shower favor to pin on their clothes. Normally, you are not allowed to cross your legs or arms because somebody else might catch you and steal your favor. A variation of this game is to have the word "baby" be the taboo word. If somebody says that word, in any language, you can steal his/her favor. The person who has the most favors at the end wins.
Ideas to save money: 1) feel free to shop at 99 cents stores. Many of these stores tend to have a variety of baby shower favors, and you can buy cheap supplies for the games, such as balloons. 2) Clean up your closet and don't feel bad about regifting items as prizes. 3) Another idea is to join your community's freecycle group in yahoo and ask if anybody has anything that they can donate for prizes or even activities (such as candles, wine bottles, coffee, porcelain items, etc.) If you don't know what I'm taking about: the freecycle group is a group of people that offer items that they no longer are going to need or use (many times those items are new or almost like new) to the other members of the group. The people who are interested reply, and the lucky one is the first one to reply and pick it up. It's on first-come first-served basis. You can also request things that you need or want, or borrow items. I belong to the Conejo Valley Freecycle group, and the members are very generous and nice. 4) If you don't want to give intricate prizes, you can have a standard prize that you give to everybody. I went to a baby shower once where the prize was a plastic baby bottle filled with candy.
I hope that all of this is helpful. Good luck in your baby shower and have fun!