Depends on the type of tree and depends on what you mean by "severely". Can you enlighten us further?

pic of tree.. and leaf ... to get an ID ... then we can discuss whether it needs pruning ...

is this something you can do yourself.. or will you be hiring it out ...

ken

Right^. The use of the word 'severely' by definition indicates an overzealous attack on the trees. They will-as trees always have-respond to the loss of numerous branches by attempting to right this loss. We call these suckers. Where there was one branch before, now there might be sixteen, all trying to develop around the same growing point. Much does depend on species, but when you say severely, no, that won't work for anything. Might coppicing be an option? That way, you'd end up working with all new stems, not mangled and abused things.

For trees which are still basically in good shape but which have been long neglected, the "crown cleaning" that may be needed should be done taking into consideration that the tree has not had work done to it in a long time, and that therefore, they should be brought around gradually. Anything which lops off lots of foliage at any one time is likely to do more harm than good, but many tree species will resprout from the complete loss of above-ground parts.

You mention that the trees haven't been pruned 'properly' because of crossing branches, water sprouts and crossing limbs and then you mention perhaps these problems can be solved by severely cutting them back. What's your definition of properly, because cutting them back is just going to make all of the above worse.

What kind of trees do you have. Do you have a picture or two? Where do you live?

In general mature trees don't cope well with heavy pruning.

Wrongs Done to Trees

http://www.plantamnesty.org/assets/docs/4a2%20wrongsdonetotrees.pdf

Hire an ISA certified arborist.

"Can I cut them back severely?" (Screaming Inside)

Now, I don't trust you, and you shouldn't trust yourself. Pictures of the so called "overgrown" trees would be very helpful. In general, remove dead, diseased, broken branches and watersprouts.

Also, autumn is generally a bad time to prune.

That would depend on where the OP is located. It is fine to prune in Autumn and throughout the Winter in some climates.

Depends on what kinds of trees these are.

Thats also true.

And the type of pruning and that depends on your objective. Do you want fruit? To eliminate a danger or obstacle? Obtain, or maintain a view? When will it be pruned again? Improve the form?

As a landscaper I did a lot of yard makeovers which involved a lot of pruning. Most of it came down to shrinking shrubs and trees. Antique-ing, I called it. Aka Nawiki. Sorta like giant bonsai with a lotta latitude. A real fun approach to pruning. It requires regular follow up though.