If you can get your hands on yesterday's WSJ, turn to page D1 and read Sue Shellenbarger's "Work & Family" column with this title. She writes about the special ways that dads positively impact their children, even if they are not able to spend as much time with them as mothers sometimes are, especially when the children are toddlers, but later as well.
For one thing, dads get physical with their children in a way that mothers don't. This was called "rough-housing" when I was growing up, and it was fun to rough-house with the boys, even when they were tiny. (I was more reserved with Mary. She's a girl, after all.) We would "wrestle", rolling over and over on the floor, with my protecting them with my elbows as my embrace trapped them against my chest when I rolled on top. That was great fun.
Another thing she mentions is that dads talk to their little ones differently. They tend to talk to them as they would to grown-ups. I remember that too. I would intentionally use adult words that I knew they wouldn't know, just to get them at least familiar with the sound. And then I would give them longer answers to their questions than one might expect. If an answer led to another topic, then I would discuss that topic. (At the very least, this approach would lead them to thinking about taking a nap as Dad dronned on and on and on.)
She mentions playing games. (Not board games!!!!) Hide and seek was really fun. Once I had a couple of two way radios, and put one in a closet and then I hid elsewhere in the house. As they were getting close to my hiding place, I would whisper in my radio, and it would make a sound where I had hidden the other, and off they would go!
We also had a really grotesque halloween mask, one that would fit over one's entire head, and I would put it on a soccor ball. Then I would put it in various surprising places and scare the heck out of them when they opened a closet door or a drawer or whereever. One night, before they went to bed, I put the thing on the pillow of one of the boy's bunks, and pulled the covers up to it after placing other pillows under the covers to make the shape of a body. Another night I propped the thing outside their bedroom window, looking in.
Then she mentions how dad's deal with behavior. She said that they are more likely to warn a child about "real-world" consequences that would attend bad behavior than mom's. I recall warning one of my children that his/her unfriendly behavior to his/her sibling(s) could result in their not being friends when they grew up. He/she took that seriously I think, and they are now great friends. Or maybe they would have been great friends anyway. (After all, they obviously had a common enemy.)
If you are a dad, you will find that article very encouraging and not feel so bad about spending less time with them than, perhaps, their mother. That sounds like the old "quality time" excuse, but I think Ms. Shellenbarger has a point. (We had a joke about quality time vs. quantity time around our household. When the kids and I were just goofing off, we called that "quantity time" and loved it.)