A common question for many converts is whether they can make aliyah to Israel. In short, yes, a convert from any movement can make aliyah to Israel under the Law of Return. This means the convert can get expedited citizenship and be labeled as a "Jew" on their ID card. (I'm still very confused by the labeling of people by religion as an ethnicity on the ID cards. Any Israelis care to explain that one to me??)
However, things get trickier. The problem is that the convert-related regulations and policies aren't being made public, so over the last couple of years, converts have had to collect anecdotes and try to figure out what the rules are behind the scenes. (The Jewish Life Information Center has been the most successful at this collection process.) Even worse, whatever policies exist seem to be applied in a haphazard fashion, based on the person doing the enforcing.
For one (and I welcome any further explanation!), converts are required to remain in the community of their conversion for one year after the mikvah. This is a requirement of the Ministry of the Interior, NOT the Rabbinate. Thus, the Rabbinate may be fully willing to recognize you as a valid convert and Jew, but the state bureaucracy may deny you citizenship under the Law of Return for failure to prove yourself to be a Jew!
(1) Your rabbi will be required to write a letter detailing your conversion process and your involvement in the community after the conversion. What's more uncertain is that supposedly now your conversion must have taken a minimum number of hours (350 it seems), which must be supported and detailed by your rabbi in his/her letter. I guess if it didn't take that many hours, you're banned from ever making aliyah?? Further, I know that some female rabbis have male counterparts actually be the converting rabbi and letter writer simply to avoid making the convert's life any more difficult. A sadly practical move.
(2) You'll also have to write a letter about your conversion process, and it sounds like a long one. You'll need to discuss why you decided to convert, your conversion process, and your involvement in the Jewish community since conversion.
(3) As you might imagine, you will need to provide a valid copy of your conversion certificate.
What worries me? The "one year in the same community after conversion" requirement. I haven't seen anything written about this, but what happens if someone does move to a new community within that one year period, and then decides to make aliyah 10 years later? Are they permanently banned from making aliyah because of a decision made with no consideration of aliyah? Worse, this requirement was ruled an unconstitutional limit on the Law of Return by the Israeli Supreme Court (in either 2006 or 2007, if memory serves), but the Ministry of the Interior reinstated the policy secretly less than a year later. About a year ago, they admitted publicly that the policy was back in place because of work by organizations on converts' behalf. I am unaware of any new legal challenges to it. Both as a convert and as someone studying the law, the chutzpah (audacity) of a government agency to violate the law makes me more than a little angry!
Speaking of the law, the problem with non-orthodox converts is when family law comes into play. Marriage is what gets all the attention, but this would involve anything status-related. Status can involve anything family-related, such as marriage, divorce, child custody/support, inheritance, or even if there are special laws for torts (injuries) between family members. Israel's status-related court system is a religious court. There are four parallel court systems: Jewish, Christian, Muslim, and Druze (if you don't know the Druze, look them up, they're very interesting!). Americans and Europeans with conversions not recognized by the Jewish courts will be thrown into the Christian courts even though they are not Christian. Similar converts from Muslim-heavy nations will likewise be placed in the Muslim courts (and maybe also converts with Muslim-area heritage who happen to live in America or Europe). You would also not be allowed to be buried in Jewish cemeteries, as far as I understand.
Note that even some orthodox converts may be questioned! Nowadays, it seems all converts are questioned, regardless of converting beit din. Though it may change at any time, there is now a list of "presumptively valid" converting batei din. Of course, once you have citizenship, these issues should no longer affect you.
Now for my 2 cents from my personal experience. I had originally planned to make aliyah upon law school graduation, which would have been well over a year after my conservative conversion. This was the plan while I was completing my conservative conversion, though of course plans changed when I began to consider an orthodox conversion! Now my plan is very different, and a bit undefined at the moment. However, the point is that my Jewish Agency shaliach stopped returning my emails as soon as I began asking questions about how my conservative conversion would affect aliyah. We had communicated several times before that, and then email after email went unanswered. As you might imagine, now I'm more than a little gun-shy about dealing with Israeli bureaucracy, and it is already the source of pain and frustration for me. Sadly, I don't think this is an isolated case.