First of: the muslims that occupied Spain weren't Arabs, were North africans. That's actually a big mistake, since Arabs are the ethnic peoples who live in the Arabic peninsula and in other close regions.
Now, for the real answer: Yes, there is some genetic similarities of modern spaniards and Northafricans due to the muslim ocupation of Iberia (that lasted a whooping 8 centuries before complete expulsion in 1492). But, the answer isn't simple as that, because at first muslims that emigrated to Iberia in the early stages of the occupation were few, and mainly ranked as elite people and nobles. And in 1492, all the muslims (and with them, most of the northafrican ethnicity) were deported back to africa.
Now the studies:
http://mbe.oxfordjournals.org/content/21/7/1361.full#F04 http://www.rootsweb.ancestry.com/~wellsfam/dnaproje/haplogroupR.html
Study reveals that the North african contribution to the spaniard male gene pool wasn't bigger than 5.65%.
http://www.ncbi.nlm.nih.gov/pubmed?uid=16201138&cmd=showdetailview&indexed=google
Other study reveals that the main haplogroup U6 (regarded as nothafrican) was the biggest in the southern part of Iberian, and the southern parts of Spain and Portugal alike, more prevalent than other european countries. Which mainly states another empiric hypothesis: Iberians have the most north african admixture than any other european group. Yet again, the U6 is very scarce getting an approximated 8% along iberia, and getting a maximun of 10% in the southernmost regions.
On the other hand, as well, the genetic mix of Subsaharian genes in the iberian genepool is the biggest than other parts of Europe, being the most important in Portugal. This can be explained due to the bringing of slaves in times of muslim rule in iberia, as well with the berber migration to the peninsula. http://web.archive.org/web/20080820125442/http://en.wikipedia.org/wiki/Sub-Saharan_DNA_admixture_in_Europe
Another study has linked that there is more genetic makeup of middle eastern and furthermost oriental mediterranean, linking other peoples that inmigrated to the peninsula, mainly sephardic jews, or other medieval peoples that andalusian sources designated them as "sirians", or even much more ancient, like fenicians and greeks. This genetic contribution has been greater in the oriental mediterranean coast of Iberia, and the balearic islands, making 10 genetic contribution from the oriental mediterranean and up to 20% in the oriental coasts of iberia (spanish side). Even greater than north african genetic contribution.
http://www.cell.com/AJHG/abstract/S0002-9297(08)00592-2
Finally another study has concluded that the region with the least genetic contribution of northafrican was Castilla-la mancha (center-south), while the 3 regions with most genetic contribution from North africa are Galicia (North-west), Andalucia (south) and Balearic islands (mediterranean). http://www.elmundo.es/elmundo/2008/12/04/ciencia/1228409780.html
Tl,dr: Genetic contribution of Northafricans is 5-10%, being 10% in the south, galicia and balearic, while oriental mediterranean (sephardic jews, fenicians, greeks, etc) genetic contribution ranges 10 to 20%, being 20% in the mediterranean western coast (Valencia, Balearic I. and Cataluña). Subsaharian contribution is very little but present in the southernmost west part of andalucia, representing up to 3-5% in that region only.
Basically they do not look like arabs, they look like meds, because meds are very similar from one another, mainly because of all the inmigration and trading there has been around in the mediterranean for centuries. Also spaniards have a lot of genetic make up from the original peoples of Iberia, and Celts, much more than any other genetic contribution from the mediterranean.