Cheap Screw-Valve Connectors for Water-Based Crafts
Here are a couple of simple, inexpensive solutions.  It doesn't beat the free materials cost of recycling used stuff, but it also doesn't require all of the labor to fabricate water-tight connections.  


Materials for the first solution would be under a dime per connection based on roughly 1/4" ID plastic tubing.

Get some metal tubing that fits tightly into the acrylic tubing.  It can even be slightly larger than the inner diameter because the plastic tubing can be warmed and stretched.  Copper tubing is fairly inexpensive, and a small roll goes a long way (a 10' roll of 1/4" OD copper tubing is about $5 and will yield 80 connectors).  Cut some pieces roughly 1.5" long.  

If you use a tubing cutter, the end will be a little rounded, which is perfect.  If you cut the tubing by other means, use a little sandpaper to smooth any rough or sharp edges, including the end, since these will weaken the plastic tubing.  Use a permanent marker to draw a line around the circumference at the halfway point.

Insert a piece half way into one side of the plastic tubing to be joined.  Leave the mark visible.  The water isn't under serious pressure, so if you need to stretch the plastic tubing a little, it will probably be water-tight as-is.

If you needed to warm the plastic tubing, wait for it to cool.  Finish the connection by pushing the other side of the metal tubing into the other piece of plastic tubing until the ends of the plastic tubing meet.  The visible mark will let you know if you're pushing the metal tubing farther into the first piece, which you don't want.  

If that happens, reposition the metal tubing to the halfway point.  Use a plastic zip tie to tighten the plastic tubing on the first side (under 2 cents if you buy a package of a reasonable quantity).  Position it at half the inserted length of the metal tubing, and use needle nose pliers to pull the zip tie tight (pull it tight by hand, then grab the end with pliers close to the lock, and rotate the pliers against the lock for leverage to pull it tighter).  You can snip off the tail.  The zip tie can be used in any case for extra insurance of a water-tight connection.

On the second side, if you want to add a zip tie, use the removable type there, which will facilitate disconnecting and reusing everything without risking cutting the plastic tubing when cutting off a single-use zip tie.
If you need a ton of connectors and want to save all labor, a ready to use solution is double-sided barb connectors.  For small diameter tubing, this would cost just over a dime per connection (in quantities of 50 or more), with zero fabrication.

Image courtesy Home Depot

  

You just work the tubing over the barb.  This is intended for a permanent connection and doesn't require any form of clamp; it isn't designed as a quick disconnect.  You can disconnect it, but you will probably need to warm the tubing to soften it, then push the tubing off rather than pull it off (think Chinese finger trap).  

If it is an application where you will need to connect and disconnect often, I don't know how well the tubing will hold up to that.  If you use these connectors, I would leave the tubing a number of inches longer than required.  If the connection stops being water-tight due to disconnection/reconnection, snip off the worn end of the tubing to connect a fresh end.