You can't have just any subplots, however. The subplots, as mentioned earlier, should be chosen to support the main plot, instead of distracting from it. Consider the obligatory love interest in pretty much every movie: sometimes it suits and supports the story; sometimes it doesn't and is distracting and annoying.
Having too many subplots, too many stories happening at once, can be confusing to a reader who isn't dedicated to unravelling the tangle. If your intent is to have something that needs careful tracking to follow, then by all means have a larger number of subplots, but take care in choosing them, and make sure you know what you're doing and why. Also keep in mind that "too many" is a very subjective thing, and both the number of threads and your skill in weaving them together will move the "too many" threshold around differently for different readers.
Sometimes it's easy to tell when you have thrown in "everything but the kitchen sink". A lot of the novels written during November suffer from this, as participants madly pad their wordcount. More often, it isn't so easy. When you get down to it, you should look at everything in your story and ask yourself if it really belongs, both at the scene and detail level.
On the scene level, try asking yourself if the goal of a particular scene advances the main plot or a subplot, which one, and how. If it doesn't, remove it. (Save it someplace outside your novel for safe keeping; I wouldn't ask you to delete words that may come in handy later.) The 'how' is important too! If you aren't sure how it advances the plot or subplot, but know it's related, flag it for consideration. With a bit of massaging, it may be a keeper; sometimes tying it to another scene, or adding or removing aspects will let you keep the bits you want and let them advance the plot.
In my opinion, a scene that does a lot of character building but does not advance plot should go. Those bits that show the character to the reader should be kept in mind, sometimes kept verbatim, and inserted as appropriate into scenes which do advance plot. Some of the best characterization comes from showing how a character deals with one of the plot challenges, or pieces of information, or an early encounter with the antagonist.
Within a scene, the details and actions should also be looked at carefully. Does a particular detail or action advance a plot or subplot, or show us something relevant about a character, situation, or location? The shorter the piece, the more important this question is, but it should still be asked about an epic novel. Those should be epic because they have a lot of story, not because they have a lot of irrelevant detail!
Once you've identified your problem areas, you're most of the way to fixing them. Remove (but as I said above, don't delete) those scenes or details that are irrelevant. Rewrite, expand, combine, or rearrange those that are relevant but not a definite advance - keeping in mind the questions above that let you find these parts while you are writing the new versions.
For example, consider a short scene where two characters are catching up or sharing their plans for the day, which include actions that will be plot-relevant later on, but who are not actually doing anything in that scene that advances the plot. The information in their conversation could be inserted into a scene shortly after the original scene's position which does advance the plot, perhaps as a brief memory of the key information given when it becomes relevant, or an indication that the character is waiting for the other party to arrive or send word that something is done. You wouldn't want to do this for a critical plot point or the climax however, as that's getting into Deus Ex Machina territory. In that case, you'd have to work the information into an earlier plot-advancing scene, so the reader knows about it even if they don't think it's important at the time.