I use Testors Cement for Plastic Models (the red tube) and I keep the cap on. When not in use, I put a small plastic bag over the tip and hold it on with a rubber band. The bag is just one I got in the box for one of my Kato buildings. The glue in the tip will eventually harden, but it won't stick to the bag. When it dries, I peel the glue off the bag. If I'm in the middle of using it and need to set the glue down, I just rest the tip inside the bag. If it drips, I let it dry and peel it off.
I really like this glue because it still gives me enough "play" to adjust when using it, but it dries enough, quickly enough to make modeling super easy. I was able to build 2 models in about 3 hours the other day, just because of the glue.
Glue:
http://i.walmartimages.com/i/p/00/07/56/11/35/0007561135090_500X500.jpg (value pack at Hobby Lobby is under $5)
For applying the glue, I use the tip of the applicator that comes with the tube for larger beads. For smaller details, I use Microbrush Applicators. The come in various sizes and I use the superfine ones. They come with 10 disposable applicators in a pack for $1.99 at hobby lobby.
Applicator Link:
http://thebluebottletree.com/hobby-store-find-microbrushes/
You can reuse them by cleaning the tip with nail polish remover.