How fast can you get indexed?
 

I noticed that the pages of my site are put into the google's index only a couple of pages at a time.

I never noticed this before. Do I need to worry about this or is it normal for google?

Do you use a sitemap?

Yes. Everything is in listed in the sitemaps (xml and txt version). The pages are interlinked, too.
It looks to me as if the spider either looses interest after a few pages or google crawls the pages but puts them into their index only a few pages at a time.

its perfectly normal for a new site. Get more backlinks to your site and internal pages to have them indexed too.

PS.

How many pages google indexes depends on many factors, major ones are:
(in high to low importance order, IMO)

1) Unique content.
2) Number of external links to homepage.
3) Number of external links to internal pages.

A couple of days to a week.

With a sitemap you can get listed very quickly.

From 30 minutes to 1 hour ;)

You don't need a sitemap at all if your site is well made, with great linking structure and so on. If your site is new, just wait a bit or update your content more often.