Amidst the discussion (which I though went pretty well, with valid points from probably everybody who contributed) there were some good suggestions. Let me summarise them for you.
Buildcraft pipes with insertion pipes: Buildcraft pipes in general have a completely different logic than tubes in that at the point when items enter the pipe network they don't care whether or not there is a valid destination. However you can mimic some of the behaviour with insertion pipes, which will attempt to place an item in a valid inventory. You will still need an overflow system at the terminus of your pipe network, or a loop back to the input (which can be acheived in one block with an iron pipe pointing back into the pipe the items came from). But, wasn't it best practice to have overflow protection for tube systems too. Diamond pipes and iron pipes will be important tools to control the flow of items. Autarchic gates can be used to pull items out of chests. Gates are really useful to stop autarchic gates spamming your pipe network even if there is no inventory.
Infinitubes: They are instant transfer tubes that may seem a bit strange to the uninitiated. The magic happens in these blocks called teleposers. In there simplest forms they can be used like chickenbones translocators in that they can pull items from an inventory on their input side and place them in an inventory in their output side. This requires no power and the in/out sides are configurable. They can also do this over longer distances between connected teleposers, connected by transport conduits. This does require power through the transpressurizer. Power needs to be applied by EU or MJ to any side but the top of the transpressurizer. Put a transport conduit on top of the t.pressurizer and connect it to your network. Every teleposer connected via tubes to the t.pressurizer will now be powered. Power is charged per transaction. You can disable power requirements in the config. The teleposers have filters, that allow you to include or exclude items . You can also label your teleposer with a text string of your choosing and it will be paired with other teleposers that you also give that string. You can also set priorities for teleposers which I find very useful.
Transfer nodes/pipes, Extra utilities: Uses vanilla hopper mechanics and extends their use to to having pipe a pipe network and also liquid and energy (mj) support. Place an item transfer node on an inventory and it will pull the contents out into its one slot buffer. Then it will search the network for a valid inventory. You can manipulate the way the transfer node searches for items by using a wrench to make the pipes have iron pipe like functionality or sandstone pipe functionality. If you want to you can upgrade a pipe to a filter pipe which works like a diamond pipe. Initially they only accept one item but you can use item filters to program more items for a specific route. Just put the card in the right slot. Finally, there are sorting pipes. They will prevent an item from being placed in an inventory unless said item is already present.
Conveyor belts: The final option works very well for some systems. It can distribute items insertion pipe style through into barrels or DSUs by placing an item collector above the barrel and a belt above that. You can just as easily do this with chests and use an item router and select your items to be pulled down. The item router is very good at routing items for both conveyor belts and buildcraft pipes. Conveyors will spit items out onto the floor at the end of the line unless if you terminate it properly with an item collector and an inventory like an Iron chest. If you need to you could have several termini using the barrel method I described but replacing the barrels for diamond chests if you want a really big overflow buffer. I tend to use conveyor belts to perform smaller specialised tasks and often have them in support of pipe networks. I wouldn't personally use them for replacements of the extensive pneumatic tube networks we all used to create but they are very good and cool.
Applied Energistics: I think it is pretty well know what this mod can do. However I wouldn't consider it to be a true replacement for pnemotubes in the extent that they require alot of power to run and their costs inhibit large networks (until you have enormous resources and don't care). That being said, maybe it is just my playing style because seem people seem to make effective use of large systems even with the dreaded import bus (just ignore my irrational dislike there
)Logistics pipes: Really complex but very flexible and really powerful. I am too tired to explain it.