Although the answer to this question may seem simple, it recurs with alarming regularity on aspie forums everywhere. Often, it is confused with the aspie's ability to find a partner or the famous aspie empathy problems - these are different things altogether which I'll hopefully discuss in follow-up posts.
Emotional Behavior in Aspies
Aspies are very capable of loving but they often confuse the issue by adopting an altogether too rigid view of love. Despite popular mis-belief, aspies are generally fairly emotional beings. We have intense feelings of happiness and even more intense feelings of sadness. The smallest triggers can produce huge emotional responses in us. While a bad day at work may make an NT grumpy, it could make an aspie feel suicidal. Similarly, when something good happens an aspie may seem to be over-reacting or overly happy. Most aspie adults have long since learned to control excessive displays of happiness but it's very apparent in aspie children with jumping, shouting and singing.
Aspies seem to categorize love as one of those mostly unattainable permanent states of extreme happiness directed at a single person. Such a state is not attainable with all partners and certainly isn't sustainable over long periods.
Expectations of Love
When an aspie who has experienced love in this manner discusses the question of "what is love" with his or her NT partner, they may be quite disappointed with the response. To an NT, love is more about respect, commitment and other semi-tangibles, while an aspie may respond that it's the feeling you get when you look at your partner's smile and it warms your face like when the sun is shining on it. To an NT, this is just poetry but to an aspie it's reality.
The sad thing about this is that in an NT/Aspie relationship, since neither partner has the same view of love, they give eachother what they need, instead of what their partner needs. Aspies don't need unwavering respect and commitment, they need smiles and hugs. Of course, when the aspie greets/reassures his or her partner with a smile and a hug instead of words/promises and kisses they're likely to offend. The same is true for NT partners who shout or scowl a lot.
Measuring up to Expectations
Aspies who have been in love but have become separated from their lovers are often so fixated on the feelings of the previous relationship that they can't move on and won't give anyone else a chance to get close to them. They may declare that the previous partner was the only one for them or that they're only looking for a new partner who is "exactly the same".
Similarly, as mature relationships cool off, the aspie may mistake the loss of the "constant euphoria" sensation as a withdrawal of love. When this happens, they will need a lot of reassurance. This is particularly important when you have your first child. There are widely documented cases of partners (husbands particularly) who feel "squeezed out" of the relationship with the birth of children and subsequent change of focus to concentrate on the child. For an aspie, this change of focus is even more extreme.
I guess the main point of this post is that aspies can certainly give and receive love but that their expectations are often too high or too focussed to enable them to be properly receptive. It also takes a very special kind of NT to give an aspie the sort of love they need.