I'll give you a good example of some 'neat' ways this can be applied. I have a community site for private sperm donation, where donors and recipients look for and meet each other. Kind of like a social dating site, only for making babies.
I have several functions that rely on users being in one group or another from the point of registration.
1 - My users rely heavily on proximity searches. I use a third party CB geocoding module to show a map of users (Geommunity), and one of their cool features is to show a map of users based on group membership (I just got the developer to update this to work with GJ2.0) This is SUPER helpful for women who are looking for a donor as they can visually see what donors are closest to them on the map. Obviously this map doesn't work if the users aren't added as soon as they register
2 - I have private groups set up, one for women and one for donors, so they can ask questions without the "other half" seeing them. This is important especially for the ladies, and I want them in the group right away so they know it exists. Many of them come in with questions as to whether it's even something they would consider and just want to talk to other women.