Is the size of the genome across species roughly the same?
Chart of C-values (the mass of DNA in a single haploid cell); there is no logical order to the groups:



[source]

Base pairs in haploid genome (some examples):


Escherichia coli (bacterium): ~4.5 million
Caenorhabditis elegans (nematode worm): ~100 million
Homo sapiens (we all know what these are): ~3 billion
Pinus taeda (coniferous tree): ~22 billion
Prorocentrum micans (single-celled algae): ~245 billion


From these data we can conclude:


Different species do not have the same genome size. 
Genome size is not correlated with complexity. Organismal complexity can be hard to define but, qualitatively, I think we can all agree that a human is more complex than a single-celled alga. And yet, humans have a genome that is 80 times smaller. This is known as the C-value paradox. Note, however, that this paradox has been resolved after it was found that the genomes of most eukaryotes contain a large proportion of non-coding and repetitive DNA.




Further reading:

The C-value paradox, junk DNA and ENCODE by Eddy SR

Eukaryotic Genome Complexity by Pray L